tribological, thermal and kinetic characterization...
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Tribological, Thermal and KineticCharacterization of Dielectric and Metal
Chemical Mechanical Planarization Processes
Item Type text; Electronic Dissertation
Authors Sorooshian, Jamshid
Publisher The University of Arizona.
Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.
Download date 08/06/2018 02:18:56
Link to Item http://hdl.handle.net/10150/194809
TRIBOLOGICAL, THERMAL AND KINETIC CHARACTERIZATION OF
DIELECTRIC AND METAL CHEMICAL MECHANICAL PLANARIZATION
PROCESSES
by
Jamshid Sorooshian
________________________ Copyright © Jamshid Sorooshian 2005
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
In Partial Fulfillment of the Requirements For the Degree of
DOCTOR OF PHILOSOPHY
WITH A MAJOR IN CHEMICAL ENGINEERING
In the Graduate College
THE UNIVERSITY OF ARIZONA
2 0 0 5
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THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE
As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Jamshid Sorooshian entitled Tribological, Thermal and Kinetic Characterization of Dielectric and Metal Chemical Mechanical Planarization Processes and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy __________________________________________ Date: 4 – 4 – 05 Farhang Shadman, Ph. D. __________________________________________ Date: 4 – 4 – 05 Toshiro Doi, Ph. D. __________________________________________ Date: 4 – 4 – 05 Srini Raghavan, Ph. D. __________________________________________ Date: 4 – 4 – 05 Brent Hiskey, Ph. D. __________________________________________ Date: 4 – 4 – 05 Leonard Borucki, Ph. D. Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. 4 – 4 – 05 Dissertation Director: Ara Philipossian, Ph. D. Date
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STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an
advanced degree at the University of Arizona and is deposited in the University Library
to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission,
provided that accurate acknowledgement of source is made. Requests for permission for
extended quotation from or reproduction of this manuscript in whole or in part may be
granted by the copyright holder.
SIGNED: Jamshid Sorooshian
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ACKNOWLEDGEMENTS
I would like to begin by thanking my advisor Dr. Ara Philipossian for his divine guidance and friendship over the 5 years I have known him. He truly provided me with an experience that very few live through and I will never forget him for that. Thank you for preparing me for the long road ahead. I would also like to extend many thanks to Drs. Farhang Shadman, Srini Raghavan, Toshiro Doi (sen-sai), Len Borucki, Brent Hiskey, Dale Hetherington and David Stein for their terrific guidance over the course of my graduate work.
I would like to also thank my past and present colleagues Daniel “Yella” Rosales-Yoemans, Scott ‘DeLaNoche’ Olsen, Patrick Levy, Erin Mitchell, Leslie Charns, Lateef Mustapha, Benjamin Gray, Masano Sugiyama, Deanna King, Juan “Jesus” Weaver, Kelly Brink, Zhonglin “Z” Li, Hyo-Sang Lee, Yasa Sampurno, Yun Zhuang, Manish Keswani, Yoshiyuki Seike, Jesse Cornely and Yoshiyuki Nishimura. In particular I would like to thank Darren “D2” DeNardis. Through THICK and thin he has been a great friend, colleague and roommate and I wish him the best of luck in his journeys ahead.
To the faculty and staff. I have been in the Department of Chemical Engineering for eight years. Everyone who has come and gone has been a significant help to me. I have had the incomparable chance to interact and know each of you not only as a student, but as friends. I would like to thank Arla Allen, Nina Welch, Joe Leeming, Karen McClure, Alicia Foley, Charlotte Hamilton, Eric Case, Lorenzo Lujan and Cindy Asher for their kind help. I would especially like to thank Rose Myers who has been the kindest and sweetest person to me. I will never forget your friendship. To Drs. Baygents, Saez, Blowers, Ogden, Muscat, Arnold, Ela, Farrell, Peterson, White and Guzman. Thank you for your inspiration, motivation and teaching. I would also like to thank Dr. Jost Wendt for his amazing academic and research guidance during my undergraduate years.
To all my friends: Ashley DeNardis Jeremy Hollingsworth, Felipe Rengifo-Uribe, Michael Cramer, Ahn Quach, Pieter Rowlette, Mike Schmotzer, Worawan “I’m Kay” Maketon, Jun Yan, Paul Safier, Tom Sounart, Bob Timon, Roger Apodaca, Robert Anderson, Alison Olcott, Jessica Finley, Adam Higgins, Scott Lundwall, Michael Rhee, Joe Durgin, Nate Snow, Steve Erickson, Danny “El Camino” Sanchez, Rosemary Galhotra, Jessica Haley, Elizabeth McKey, Jenny Parker, Jenny Gain, Michael & Jill Johnson, Ali Farid, Ali “The Boss” Scotten, Armand “New Guy” Navabi, Behzad “Fun Bobby” Adeli, David “Darkness” Mwewa, Armin “The Gene” Hojati, ‘Jakesh’ James Jones and David “The Led” Eberle. I thank you all for keeping me sane amidst all the stresses and pressures in life. I would also like to thank Roxy Varza. Roxy, although I have no idea what future lies ahead for you, I wish you the happiest of lives. You were the biggest influence in my life and have shaped me in a way no one else has. Thank you.
Finally, I would like to give my greatest thanks to my family. My brother Armin (Claude Bahls), my mother, Shirin (Cheryl) and my father, Soroosh (Sam). You have all collectively inspired and encouraged to get me where I am today and there is nothing in the world that I could do or give that would make up for all the time and energy you have put into me. Thanks for always picking me up when I was down and always making me feel loved and happy. I wish you all the healthiest, happiest and most fruitful years ahead.
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TABLE OF CONTENTS
LIST OF FIGURES ............................................................................................................ 9 LIST OF TABLES ........................................................................................................... 23 ABSTRACT ........................................................................................................... 25 CHAPTER 1 – INTRODUCTION............................................................................. 27
1.1 Introduction to Chemical Mechanical Planarization ........................................ 27 1.2 History of Polishing.......................................................................................... 30 1.3 State-of-the-art CMP Processing and its Applications in Semiconductor
Fabrication........................................................................................................ 34 1.4 Equipment and Consumable Design Considerations in CMP.......................... 44
1.4.1 Pads ................................................................................................... 46 1.4.2 Slurries............................................................................................... 52 1.4.3 Diamond Conditioning Discs ............................................................ 60 1.4.4 Conventional and Non-conventional CMP Tools ............................. 65 1.4.5 Wafers ............................................................................................... 69 1.4.6 Endpoint Detection Tools.................................................................. 71
1.5 Motivation and Goals of Study ........................................................................ 72 1.5.1 Role of Applied Wafer Pressure in CMP .......................................... 80 1.5.2 Role of Tool Kinematics and Pad Geometry in CMP ....................... 81 1.5.3 Role of Temperature in CMP ............................................................ 81 1.5.4 Removal Rate Modeling.................................................................... 83 1.5.5 Cost of Ownership and Environmental Impacts................................ 88
CHAPTER 2 – EXPERIMENTAL APPARATUS .................................................... 90
2.1 Innovative Planarization Laboratory Scaled Polisher ...................................... 90 2.1.1 Polisher Scaling................................................................................. 93 2.1.2 Table Top Polishing Platform ........................................................... 95 2.1.3 Wafer Carrier and Polishing Head Mechanism................................. 95 2.1.4 Force Transducer Calibration............................................................ 98 2.1.5 Traverse Calibration ........................................................................ 100 2.1.6 Friction Table .................................................................................. 102 2.1.7 Pad Conditioning System ................................................................ 104 2.1.8 Slurry Distribution System.............................................................. 107 2.1.9 Platen Temperature Control System................................................ 109 2.1.10 Computer Automation..................................................................... 111
2.2 Sandia National Laboratory SpeedFam-IPEC Avanti 472 Platform.............. 111 2.2.1 Pad Conditioning System ................................................................ 114 2.2.2 Luxtron Motor Current Endpoint Detection System....................... 114
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TABLE OF CONTENTS - Continued 2.2.3 Platen Temperature Control System................................................ 116
2.3 Metrology Equipment..................................................................................... 116 2.3.1 Thermo-analytical Instruments........................................................ 117
2.3.1.1 Dynamic Mechanical Analyzer ....................................................... 118 2.3.1.2 Thermo-Mechanical Analyzer......................................................... 122
2.3.2 Infra-Red Temperature Measurements............................................ 126 2.3.3 Film Thickness Measurements ........................................................ 129
CHAPTER 3 – APPLIED WAFER PRESSURE EFFECTS DURING CMP ......... 130
3.1 Motivation ...................................................................................................... 130 3.2 Impact of Wafer Geometry and Thermal History on Pressure and
von Mises Stress Non-uniformity During STI CMP...................................... 131 3.2.1 Background ..................................................................................... 131 3.2.2 Experimental Approach................................................................... 133 3.2.3 Results and Discussion.................................................................... 137
3.2.3.1 Stress Simulations ........................................................................... 137 3.2.3.2 Within wafer Pressure and Stress Non-uniformity for
Nominally Flat and Thermally Untreated Wafers ........................... 140 3.2.3.3 Wafer-ring Gap Size versus Within-wafer Pressure
Non-uniformity for the ‘Central Zone’ and ‘Edge Zone’ of Bowed, Thermally Untreated Wafers ......................................... 144
3.2.3.4 Wafer-ring Gap Size versus Within-wafer Pressure Non-uniformity for the ‘Central Zone’ and ‘Edge Zone’ of Bowed, Thermally Treated Wafers ............................................. 148
3.2.4 Concluding Remarks ....................................................................... 153 3.3 Estimating the Effective Pressure on Patterned Wafers During STI CMP .... 155
3.3.1 Background ..................................................................................... 155 3.3.2 Experimental Approach................................................................... 156 3.3.3 Results and Discussion.................................................................... 158 3.3.4 Concluding Remarks ....................................................................... 163
CHAPTER 4 – IMPACT OF TOOL KINEMATICS, PAD GEOMETRY
AND TEMPERATURE ON THE REMOVAL RATE AND PROCESS TRIBOLOGY DURING ILD CMP.............................. 165
4.1 Motivation ...................................................................................................... 165 4.2 Tribology ........................................................................................................ 166
4.2.1 Stribeck-Gumbel Curve................................................................... 168 4.2.2 Sommerfeld Number ....................................................................... 172 4.2.3 Coefficient of Friction ..................................................................... 174
4.3 Freudenberg Pad Study .................................................................................. 174
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TABLE OF CONTENTS - Continued 4.3.1 Experimental Approach................................................................... 177 4.3.2 Removal Rate as a Function of Tool Kinematics............................ 180 4.3.3 Tribological Mechanisms ................................................................ 195 4.3.4 IR Process Temperature as a Function of Tool Kinematics ............ 227
4.3.4.1 1.39-mm Pad Thickness .................................................................. 227 4.3.4.2 2.03-mm Pad Thickness .................................................................. 232
4.3.5 Concluding Remarks ....................................................................... 236 CHAPTER 5 – ROLE OF TEMPERATURE DURING CMP ................................ 238
5.1 Motivation ...................................................................................................... 238 5.2 Arrhenius Characterization of ILD and Copper CMP Processes ................... 240
5.2.1 Background ..................................................................................... 240 5.2.2 Theory ............................................................................................. 241 5.2.3 Experimental Approach................................................................... 244 5.2.3 Results and Discussion.................................................................... 246 5.2.4 Concluding Remarks ....................................................................... 252
5.3 Effect of Process Temperature on Coefficient of Friction During CMP ....... 253 5.3.1 Background ..................................................................................... 253 5.3.2 Experimental Approach................................................................... 254 5.3.3 Results and Discussion.................................................................... 256 5.3.4 Concluding Remarks ....................................................................... 260
5.4 Revisiting the Removal Rate Model for Oxide CMP..................................... 261 5.4.1 Objective ......................................................................................... 261 5.4.2 Experimental Approach................................................................... 263 5.4.3 Experimental Results....................................................................... 265 5.4.4 Theory ............................................................................................. 270 5.4.5 Discussion and Conclusions............................................................ 278
5.5 Additional Flash Heating Removal Rate Model Applications....................... 285 5.5.1 Application of Flash Heating Removal Rate Model on
Tungsten CMP................................................................................. 285 5.5.1.1 Results and Discussion.................................................................... 287
5.5.2 Application of Flash Heating Removal Rate Model on the Freudenberg Pad Study ................................................................... 293
5.5.2.1 Selection of an Apparent Activation Energy for Modeling ............ 294 5.5.2.2 Results and Discussion.................................................................... 296
CHAPTER 6 – ENDPOINT DETECTION IN CMP............................................... 329
6.1 Introduction .................................................................................................... 329 6.2 Experimental Approach.................................................................................. 330 6.3 Results and Discussion................................................................................... 332
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TABLE OF CONTENTS - Continued 6.4 Concluding Remarks ...................................................................................... 344
CHAPTER 7 – CONCLUSIONS AND FUTURE WORK...................................... 346
7.1 Future Works.................................................................................................. 352 APPENDIX A – ADDITIONAL PROOFS FOR FLASH HEATING
REMOVAL RATE MODEL........................................................... 354
A.1 Modeling Proof (Courtesy of Len Borucki) ................................................... 354 REFERENCES ......................................................................................................... 361
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LIST OF FIGURES
Figure 1.1: Growth of the number of components per IC chip (Chang et al., 1996)........ 29 Figure 1.2: Size and price reduction of electronic components (Chang et al., 1996)....... 36 Figure 1.3: Step-by-step schematic of an ideal shallow trench isolation (STI)
silicon dioxide CMP process where t0 < t1 < t2 < t3 ..................................... 38 Figure 1.4: Cross sectional view of a typical interconnect line (not to scale) .................. 38 Figure 1.5: Side profile (with upper layers removed for simplicity) of typical device
isolation technologies. (a) shallow trench isolation (STI) and (b) local oxidation of silicon (LOCOS)...................................................................... 43
Figure 1.6: Side-view schematic of the CMP process for a conventional rotary polisher (not to scale)................................................................................... 45
Figure 1.7: Chemical reaction for the formation of polyurethane (http://islnotes.cps.msu.edu) ........................................................................ 47
Figure 1.8: Cross sectional SEM image of IC-1000TM polyurethane based polishing pad................................................................................................ 48
Figure 1.9: Top view of various polishing pad groove types used in CMP ..................... 51 Figure 1.10: Cross sectional SEM image of IC1400TM polyurethane based
polishing pad (top) with sub pad (bottom)................................................... 51 Figure 1.11: Schematic of a purposed removal mechanism for silicon dioxide
during CMP (Chang et al., 1996)................................................................. 54 Figure 1.12: Pourbaix diagram of a Si-H2O system (Courtesy of S. Raghavan –
University of Arizona). ................................................................................ 56 Figure 1.13: SEM images of silica slurry abrasive particulate types. (a) colloidal
silica courtesy of Fujimi Corporation and (b) fumed silica courtesy of Degussa Corporation ............................................................................... 58
Figure 1.14: Schematic of the electrostatic layer formation of an abrasive particle in a slurry solution ....................................................................................... 59
Figure 1.15: Top view SEM image of IC-1400TM polyurethane based polishing pad with flattening characteristics from a lack of pad conditioning............ 61
Figure 1.16: SEM images of resulting Freudenberg polishing pad topography (a) as received, (b) following 60-grit pad conditioning, (c) following 100-grit pad conditioning and (d) following 200-grit pad conditioning...... 62
Figure 1.17: Available diamond deposition structures for pad conditioners. (a) Electroplated, (b) Sintered grid, (c) Brazed grid and (d) Random grid. (Source: Rohm and Haas Electronics) ......................................................... 63
Figure 1.18: Mesh patterned diamond pad-conditioner (Source: ABT) ........................... 64 Figure 1.19: Top view schematic of pad-wafer geometry for a conventional rotary
polisher (Courtesy of Len Borucki) ............................................................ 67 Figure 1.20: Side view of wafer carrier head assembly digging into soft polishing
pad along leading edge of wafer (not to scale) ............................................ 68 Figure 1.21: (a) Side view of various levels of pattern design density. (b) Top-
view image of high and low density patterned structures............................ 74
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LIST OF FIGURES - Continued Figure 1.22: Step-by-step schematic of step height reduction as a function of time ........ 75 Figure 1.23: Schematic of planarization length used to evaluate polishing
performance on a global scale...................................................................... 76 Figure 1.24: Cross section of a 6-level IC design (Source: Intel Corporation) ................ 77 Figure 1.25: Side-view schematic of (a) dishing and (b) erosion during clearing
or over-polish stage of CMP........................................................................ 78 Figure 1.26: Various defect events that occur as a result of CMP
(Source: Sandia National Laboratories)....................................................... 79 Figure 1.27: COO breakdown for a typical CMP module in an IC
manufacturing setting................................................................................... 89 Figure 2.1: Scaled polishing tool at the University of Arizona’s Innovative
Planarization Laboratory.............................................................................. 91 Figure 2.2: (a) Side view schematic and (b) image of sliding friction table design ......... 92 Figure 2.3: Image of wafer carrier with poromeric carrier template ................................ 97 Figure 2.4: DC controller calibration plot for wafer sliding velocity ............................... 97 Figure 2.5: Force transducer calibration apparatus........................................................... 99 Figure 2.6: Force transducer calibration plot.................................................................... 99 Figure 2.7: Drill press with a mounted weight traverse.................................................. 101 Figure 2.8: Traverse calibration plot for applied wafer pressure.................................... 101 Figure 2.9: Side view schematic of friction table calibration set-up .............................. 103 Figure 2.10: Strain gauge calibration plot....................................................................... 104 Figure 2.11: Pad conditioning apparatus during in-situ polishing.................................. 106 Figure 2.12: Calibration plots for diamond pad conditioner (a) rotation motor and
(b) oscillation motor................................................................................... 106 Figure 2.13: Peristaltic pump flow rate calibration plot ................................................. 108 Figure 2.14: Box diagram of temperature controlled water bath system from
experiments conducted in Chapter 4.......................................................... 110 Figure 2.15: Front view of SpeedFam-IPEC 472 rotary CMP tool ................................ 113 Figure 2.16: Block diagram of an integrated Luxtron motor current EPD system......... 115 Figure 2.17: TA Instruments Dynamic Mechanical Analyzer 2980 at the IPL .............. 119 Figure 2.18: Typical DMA results for a polyurethane based polishing pad................... 121 Figure 2.19: TA Instruments Thermo-Mechanical Analyzer 2940 at the IPL................ 124 Figure 2.20: Schematic of TMA internals ...................................................................... 125 Figure 2.21: Typical DMA results for a polyurethane based polishing pad................... 126 Figure 2.22: IR camera positioned during polishing ...................................................... 128 Figure 2.23: IR image of temperature controlled polishing. Spots 1 through 10
indicate the points of temperature detection along the leading edge (SP01 – SP05) and trailing edge (SP06 – SP10) of the wafer ................... 128
Figure 3.1: (a) Diagram and (b) schematic of the Tekscan® pressure measurement sensor ................................................................................... 135
Figure 3.2: Two-dimensional contour pressure image of a flat 100-mm diameter wafer at an applied wafer pressure of 6 PSI .............................................. 136
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LIST OF FIGURES - Continued Figure 3.3: (a) Top view schematic of wafer-ring gap and (b) side view schematic
of concave and convex wafer geometries and extent of bow .................... 136 Figure 3.4: Schematic representation of the wafer stack used in the simulation model. 139 Figure 3.5: Measured pressure and simulated von Mises stress for a nominally flat,
thermally untreated wafer at 6 PSI (gap size = 1.4 mm) ........................... 141 Figure 3.6: von Mises stress simulations for 200- and 300-mm wafers at an
applied wafer pressure of 4 PSI and wafer-ring gap size of 0.4 mm......... 142 Figure 3.7: Contour pressure distribution maps for nominally flat wafers using
an as received Rohm and Haas IC-1000 flat pad and a conditioned pad (30 minutes). Note that the pad center is oriented on the top left corner of each image.................................................................................. 143
Figure 3.8: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 2 PSI) .................................................... 146
Figure 3.9: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 6 PSI) .................................................... 146
Figure 3.10: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 2 PSI) .................................................... 147
Figure 3.11: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 6 PSI) .................................................... 147
Figure 3.12: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 2 PSI) .................................................... 150
Figure 3.13: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 6 PSI) .................................................... 150
Figure 3.14: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 2 PSI) .................................................... 151
Figure 3.15: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 6 PSI) .................................................... 151
Figure 3.16: Simulated von Mises stress for a nominally flat 300-mm wafer at 6 PSI (gap size = 0.4 mm).......................................................................... 152
Figure 3.17: Flexural storage modulus results for as-received IC-1400 K-groove pad. Results were taken at a sampling frequency of 10 Hz ....................... 162
Figure 4.1: Journal bearing-shaft set-up for Stribeck model .......................................... 169 Figure 4.2: Stribeck curve for journal bearing-shaft model............................................ 170 Figure 4.3: Stribeck-Gumbel curve for CMP applications ............................................. 171
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LIST OF FIGURES - Continued Figure 4.4: Removal rate plot for 1.39-mm thick Freudenberg flat pad at a
polishing flow rate of 40 cc/min ................................................................ 182 Figure 4.5: Removal rate plot for 1.39-mm thick Freudenberg XY-groove pad at a
polishing flow rate of 40 cc/min ............................................................... 183 Figure 4.6: Removal rate plot for 1.39-mm thick Freudenberg perforated pad at a
polishing flow rate of 40 cc/min ................................................................ 183 Figure 4.7: Removal rate plot for 1.39-mm thick Freudenberg flat pad at a
polishing flow rate of 120 cc/min .............................................................. 184 Figure 4.8: Removal rate plot for 1.39-mm thick Freudenberg XY-groove pad at a
polishing flow rate of 120 cc/min .............................................................. 184 Figure 4.9: Removal rate plot for 1.39-mm thick Freudenberg perforated pad at a
polishing flow rate of 120 cc/min .............................................................. 185 Figure 4.10: Removal rate plot for 2.03-mm thick Freudenberg flat pad at a
polishing flow rate of 40 cc/min ................................................................ 185 Figure 4.11: Removal rate plot for 2.03-mm thick Freudenberg XY-groove pad at a
polishing flow rate of 40 cc/min ................................................................ 186 Figure 4.12: Removal rate plot for 2.03-mm thick Freudenberg perforated pad at a
polishing flow rate of 40 cc/min ................................................................ 186 Figure 4.13: Removal rate plot for 2.03-mm thick Freudenberg flat pad at a
polishing flow rate of 120 cc/min .............................................................. 187 Figure 4.14: Removal rate plot for 2.03-mm thick Freudenberg XY-groove pad at a
polishing flow rate of 120 cc/min .............................................................. 187 Figure 4.15: Removal rate plot for 2.03-mm thick Freudenberg perforated pad at a
polishing flow rate of 120 cc/min .............................................................. 188 Figure 4.16: Predicted removal rate (Å/min) contour plot for the Freudenberg
perforated pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI ........................................................................................... 189
Figure 4.17: Predicted removal rate (Å/min) contour plot for the Freudenberg flat pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI .............. 189
Figure 4.18: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI .............. 190
Figure 4.19: Predicted removal rate (Å/min) contour plot for the Freudenberg perforated pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI ........................................................................................... 190
Figure 4.20: Predicted removal rate (Å/min) contour plot for the Freudenberg flat pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI .............. 191
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LIST OF FIGURES - Continued Figure 4.21: Predicted removal rate (Å/min) contour plot for the Freudenberg XY
pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI .............. 191
Figure 4.22: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min at 17°C. Note that velocity is reported in RPM and pressure is reported in PSI ................................... 193
Figure 4.23: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min at 30°C. Note that velocity is reported in RPM and pressure is reported in PSI ................................... 194
Figure 4.24: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min at 47°C. Note that velocity is reported in RPM and pressure is reported in PSI ................................... 194
Figure 4.25: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min .......................... 200
Figure 4.26: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min .......................... 200
Figure 4.27: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min .......................... 201
Figure 4.28: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min .......................... 201
Figure 4.29: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min ........................ 202
Figure 4.30: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min ........................ 202
Figure 4.31: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min ........................ 203
Figure 4.32: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 43°C and a slurry flow rate of 120 cc/min ........................ 203
Figure 4.33: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min .......................... 204
Figure 4.34: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min .......................... 204
Figure 4.35: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min .......................... 205
Figure 4.36: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min .......................... 205
Figure 4.37: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min ........................ 206
Figure 4.38: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min ........................ 206
Figure 4.39: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min ........................ 207
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LIST OF FIGURES - Continued Figure 4.40: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point
temperature of 43°C and a slurry flow rate of 120 cc/min ........................ 207 Figure 4.41: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 13°C and a slurry flow rate of 40 cc/min ................ 208 Figure 4.42: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 24°C and a slurry flow rate of 40 cc/min ................. 208 Figure 4.43: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 33°C and a slurry flow rate of 40 cc/min ................. 209 Figure 4.44: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 43°C and a slurry flow rate of 40 cc/min ................. 209 Figure 4.45: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 13°C and a slurry flow rate of 120 cc/min ............... 210 Figure 4.46: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 24°C and a slurry flow rate of 120 cc/min ............... 210 Figure 4.47: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 33°C and a slurry flow rate of 120 cc/min ............... 211 Figure 4.48: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set
point temperature of 43°C and a slurry flow rate of 120 cc/min ............... 211 Figure 4.49: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 13°C and a slurry flow rate of 40 cc/min ................. 212 Figure 4.50: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 24°C and a slurry flow rate of 40 cc/min ................. 212 Figure 4.51: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 33°C and a slurry flow rate of 40 cc/min ................. 213 Figure 4.52: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 43°C and a slurry flow rate of 40 cc/min ................. 213 Figure 4.53: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 13°C and a slurry flow rate of 120 cc/min ............... 214 Figure 4.54: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 24°C and a slurry flow rate of 120 cc/min ............... 214 Figure 4.55: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 33°C and a slurry flow rate of 120 cc/min ............... 215 Figure 4.56: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set
point temperature of 43°C and a slurry flow rate of 120 cc/min ............... 215 Figure 4.57: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 13°C and a slurry flow rate of 40 cc/min ................. 216 Figure 4.58: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 24°C and a slurry flow rate of 40 cc/min ................. 216 Figure 4.59: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 33°C and a slurry flow rate of 40 cc/min ................. 217 Figure 4.60: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 43°C and a slurry flow rate of 40 cc/min ................. 217
15
LIST OF FIGURES - Continued Figure 4.61: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 13°C and a slurry flow rate of 120 cc/min ............... 218 Figure 4.62: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 24°C and a slurry flow rate of 120 cc/min ............... 218 Figure 4.63: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 33°C and a slurry flow rate of 120 cc/min ............... 219 Figure 4.64: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set
point temperature of 43°C and a slurry flow rate of 120 cc/min ............... 219 Figure 4.65: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 13°C and a slurry flow rate of 40 cc/min ................. 220 Figure 4.66: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 24°C and a slurry flow rate of 40 cc/min ................. 220 Figure 4.67: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 33°C and a slurry flow rate of 40 cc/min ................. 221 Figure 4.68: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 43°C and a slurry flow rate of 40 cc/min ................. 221 Figure 4.69: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 13°C and a slurry flow rate of 120 cc/min ............... 222 Figure 4.70: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 24°C and a slurry flow rate of 120 cc/min ............... 222 Figure 4.71: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 33°C and a slurry flow rate of 120 cc/min ............... 223 Figure 4.72: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set
point temperature of 43°C and a slurry flow rate of 120 cc/min ............... 223 Figure 4.73: Predicted COF contour plot for the Freudenberg perforated pad
(2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI ..................... 224
Figure 4.74: Predicted COF contour plot for the Freudenberg flat pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI....................................... 224
Figure 4.75: Predicted COF contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI....................................... 225
Figure 4.76: Predicted COF contour plot for the Freudenberg perforated pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI ..................... 225
Figure 4.77: Predicted COF contour plot for the Freudenberg flat pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI....................................... 226
Figure 4.78: Predicted COF contour plot for the Freudenberg XY pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI....................................... 226
16
LIST OF FIGURES - Continued Figure 4.79: Mean IR temperature readings for 1.39-mm thick Freudenberg flat
pad at polishing flow rates of 40 and 120 cc/min ...................................... 228 Figure 4.80: Mean IR temperature plot for 1.39-mm thick Freudenberg XY-groove
pad at polishing flow rates of 40 and 120 cc/min ...................................... 229 Figure 4.81: Mean IR temperature plot for 1.39-mm thick Freudenberg perforated
pad at polishing flow rates of 40 and 120 cc/min ...................................... 229 Figure 4.82: Mean IR temperature plots for 2.03-mm thick Freudenberg flat pad at
polishing flow rates of 40 and 120 cc/min................................................. 234 Figure 4.83: Mean IR temperature plots for 2.03-mm thick Freudenberg
XY-groove pad at polishing flow rates of 40 and 120 cc/min................... 234 Figure 4.84: Mean IR temperature plots for 2.03-mm thick Freudenberg
perforated pad at polishing flow rates of 40 and 120 cc/min..................... 235 Figure 5.1: Arrhenius relationship for 1-minute ILD polish on Rohm and
Haas IC-1000 k-groove pad (a) and JSR WSP pad (b). Note that units of m/s were used for the RR term on the y-axis ................................ 247
Figure 5.2: Arrhenius relationship for a 1-minute copper polish on IC-1000 XY-groove pad at a flow rate of 155 cc/min ............................................. 250
Figure 5.3: (a) Removal rate data for a 1-minute copper polish at 25°C, indicating the extrapolated dynamic etch rate across the y-axis. (b) Arrhenius relationship for the theoretically pure chemical activation energy using various dynamic etch rates at various pad temperatures. Note that units of m/s were used for the RR term on the y-axis ................................ 251
Figure 5.4: Dependence of COF as a function of average pad temperature for 90-second ILD and copper polishes at multiple wafer pressures and pad-wafer velocities ................................................................................... 256
Figure 5.5: Flexural storage modulus results for as-received IC-1000 K-groove and XY-groove pads. Tests were performed over the range of temperatures observed during polishing experiments................................ 259
Figure 5.6: Tan δ results for as-received IC-1000 K-groove and XY-groove pads. Tests were performed over the range of temperatures observed during polishing experiments..................................................................... 259
Figure 5.7: Thermal silicon dioxide removal rate data from S&H grouped by pad-wafer sliding velocities (Stein et al., 2002) ........................................ 262
Figure 5.8: Room temperature removal rates for (a) thermal oxide and (b) PE-TEOS.. 266 Figure 5.9: Lim-Ashby contour plot of the PE-TEOS removal rates in Fig. 5.8(b).
The contour interval is 500 Å/min. The grey lines show a triangulation of the individual (p,V) pairs used in the experiment in Fig. 5.8(b). The triangles are used for linear interpolation of the measured rates ............... 267
Figure 5.10: PE-TEOS removal rate as a function of p × V and platen temperature set point. Data were not obtained at 41 and 52 kW/m2 at a platen set point of 13°C.............................................................................................. 268
17
LIST OF FIGURES - Continued Figure 5.11: PE-TEOS removal rates (see Fig. 5.10) vs. the inverse of the
mean pad temperature (i.e., the average recorded IR pad temperature over the entire duration of a polish) rather than the platen set point. Data are separated by p × V. Adjacent pairs of points at each p × V ............. are replicates .............................................................................................. 269
Figure 5.12: Thermal silicon dioxide removal rate as a function of p × V and platen temperature set point. Data were not obtained at 41 and 52 kW/m2 for a platen set point of 13°C.................................................... 270
Figure 5.13: (a) Least squares fitting error of the augmented Langmuir- Hinshelwood model to the PE-TEOS data in Fig. 5.8. (b) The temperature model velocity exponent, a .................................................... 272
Figure 5.14: (a) The mechanical removal rate coefficient cp and (b) The reaction rate pre-exponential A of the model in this work....................................... 273
Figure 5.15: (a) The temperature increase proportionality constant β and (b) the required reaction temperature rise for the six p × V conditions in the PE-TEOS data ...................................................................................... 273
Figure 5.16: Comparison of the fit of the model of Eqns. (5.10) and (5.11) with room temperature PE-TEOS data at the largest and smallest values of E considered .......................................................................................... 276
Figure 5.17: (a) Plot of the model estimate of the ratio k1/k2 of the chemical rate to the mechanical rate as a function of E for each p × V condition used in the PE-TEOS data in Fig. 5.8(b). (b) Plot of the measured and calculated apparent activation energies for the PE-TEOS data from Fig. 5.11 as a function of the mean of the ratio k1/k2 at each p × V condition .......................................................................................... 276
Figure 5.18: Comparison of the model with PE-TEOS data at different platen temperatures using E from polishing condition pV3 (~31 kW/m2) ........... 277
Figure 5.19: Comparison of the model in this work (solid symbols) with TOX removal rate data at different platen temperature set points (See Fig. 5.12) using the activation energy at the most thermally limited condition (pV3).............................................................................. 277
Figure 5.20: Preston plot of TOX polishing data from S&H (open circles and squares). A theoretical fit to the data with the current model is also shown (solid triangles). See also Table 5.1. The fit was performed using a randomly selected subset of the data (circles) – the match with the remaining data (squares) provides a measure of predictive capability................................................................................... 280
Figure 5.21: Lim-Ashby plot of the thermal oxide polishing data in Fig. 5.20. The grey lines show a triangulation of the individual (p,V) pairs used in the experiment in Fig. 5.20. Contour interval: 500 Å/min .............................. 281
18
LIST OF FIGURES - Continued Figure 5.22: Lim-Ashby wear plot showing how the data from Fig. 5.21 would
have looked had the removal rate been perfectly Prestonian (i.e., if all points had been on the regression line with no scatter). The contour lines are linear approximations to hyperbolic arcs of the form p × V = const. The triangles are used for linear interpolation of the measured rates. Contour interval: 500 Å/min ...................................... 282
Figure 5.23: Map of the ratio of chemical rate k1 to mechanical rate k2 derived from the best fit of the Langmuir-Hinshelwood model to the data from Stein and Hetherington (see Figs. 5.20 and 5.21). Material removal is severely mechanically limited in the upper left hand corner of the map. Toward the right side of the map, chemical and mechanical rates are more equally balanced.............................................. 283
Figure 5.24: Apparent pressure threshold behavior at constant V and sublinear velocity behavior at constant p in the PE-TEOS data from Fig. 5.8(b) compared with extrapolations from the current model. The upper model extrapolation is performed at constant pressure (7 PSI) and variable speed. The lower model extrapolation is at constant speed (90 RPM) and variable pressure. The isolated point at p × V~44 kW/m2 (6 PSI, 60 RPM) lies on neither extrapolation because the removal rate depends on p and V individually rather than just on the product p × V. At any fixed p × V, a range of rates is possible ......................................... 284
Figure 5.25: Tungsten removal rate as a function of p × V and platen temperature set point. Data were not obtained at 25 kW/m2 for platen set points of 13°C and 24°C, as well as 87 kW/m2 for a platen set point of 24°C ........................................................................................ 288
Figure 5.26: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 13°C. The RMS between the experimental and theoretical results was approximately 200 Å/min ... 290
Figure 5.27: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 24°C. The RMS between the experimental and theoretical results was approximately 338 Å/min ... 291
Figure 5.28: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 33°C. The RMS between the experimental and theoretical results was approximately 377 Å/min ... 291
Figure 5.29: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 43°C. The RMS between the experimental and theoretical results was approximately 265 Å/min ... 292
Figure 5.30: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min .................................. 303
19
LIST OF FIGURES - Continued Figure 5.31: Experimental and theoretical ILD removal rate as a function
of p × V at platen temperature set point of 24°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min .................................. 305
Figure 5.32: Experimental and theoretical ILD removal rate as a function p × V at platen temperature set point of 33°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min .................................. 305
Figure 5.33: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min .................................. 306
Figure 5.34: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min ................................ 306
Figure 5.35: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min ................................ 307
Figure 5.36: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min ................................ 307
Figure 5.37: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min ................................ 308
Figure 5.38: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min .................................. 308
Figure 5.39: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min .................................. 309
Figure 5.40: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min .................................. 309
Figure 5.41: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min .................................. 310
Figure 5.42: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min ................................ 310
Figure 5.43: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min ................................ 311
Figure 5.44: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min ................................ 311
20
LIST OF FIGURES - Continued
Figure 5.45: Experimental and theoretical ILD removal rate as a function of
p × V at platen temperature set point of 43°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min ................................ 312
Figure 5.46: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min ....................... 312
Figure 5.47: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min ....................... 313
Figure 5.48: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min ....................... 313
Figure 5.49: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min ....................... 314
Figure 5.50: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min ..................... 314
Figure 5.51: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min ..................... 315
Figure 5.52: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min ..................... 315
Figure 5.53: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min ..................... 316
Figure 5.54: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min ....................... 316
Figure 5.55: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min ....................... 317
Figure 5.56: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min ....................... 317
Figure 5.57: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min ....................... 318
21
LIST OF FIGURES - Continued Figure 5.58: Experimental and theoretical ILD removal rate as a function of
p × V at platen temperature set point of 13°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min ..................... 318
Figure 5.59: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min ..................... 319
Figure 5.60: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min ..................... 319
Figure 5.61: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min ..................... 320
Figure 5.62: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min.................................. 320
Figure 5.63: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min.................................. 321
Figure 5.64: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min.................................. 321
Figure 5.65: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min.................................. 322
Figure 5.66: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min................................ 322
Figure 5.67: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min................................ 323
Figure 5.68: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min................................ 323
Figure 5.69: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min................................ 324
Figure 5.70: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min.................................. 324
Figure 5.71: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min.................................. 325
22
LIST OF FIGURES - Continued Figure 5.72: Experimental and theoretical ILD removal rate as a function of
p × V at platen temperature set point of 33°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min.................................. 325
Figure 5.73: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min.................................. 326
Figure 5.74: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min................................ 326
Figure 5.75: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min................................ 327
Figure 5.76: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min................................ 327
Figure 5.77: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min................................ 328
Figure 6.1: Raw platen motor current output (Channel A) for an over polish run from STI patterned wafer Set C........................................................... 334
Figure 6.2: Endpoint detection viewing window with specified dimensions ................. 337 Figure 6.3: Typical conditions for endpoint detection using an “Interference”
signal type and End of oscillation stopping point...................................... 338 Figure 6.4: Typical conditions for endpoint detection using a “Falling Slope”
signal type and End of slope stopping point .............................................. 338 Figure 6.5: Motor current signal for polished wafer from Set A with an
applied endpoint recipe (left). Motor current signal for polished wafer from Set B with an applied endpoint recipe (right) ......................... 339
Figure 6.6: Motor current signal for polished wafer from Set C with an applied endpoint recipe (left). Motor current signal for polished wafer from Set D with an applied endpoint recipe (right) ......................... 340
Figure 6.7: Pattern density distribution for STI patterned wafer Set C .......................... 343 Figure 6.8: Pattern density distribution for STI patterned wafer Set D.......................... 343 Figure A.1: Polishing pad scanning profilometry data showing evidence of an
exponential right hand tail (Borucki et al., 2004)...................................... 359 Figure A.2: (a) Pad heat partition factors as a function of sliding velocity and
asperity contact dimension. (b) Pad heat partition factor proportionality constant and velocity exponent......................................... 360
23
LIST OF TABLES Table 1.1: Characteristic physical properties of IC-1000TM polyurethane
based polishing pad (Oliver, 2004).............................................................. 49 Table 1.2: Material properties for common abrasives in slurries (Oliver, 2004).
*(Source: S. Raghavan, University of Arizona, Tucson, AZ) ..................... 57 Table 2.1: Scaling parameters for 1:2 SpeedFam-IPEC 472 scaled polisher ................... 94 Table 3.1: Wafer stack material properties assumed in the simulation model ............... 139 Table 3.2: Apparent activation energy values for HDP filled STI wafers of
variable pattern density .............................................................................. 159 Table 3.3: Derived effective pressure values for STI polishes at a platen
temperature of approximately 10°C. The values represent an average of four individual polishing experiments................................................... 159
Table 3.4: Derived effective pressure values for STI polishes at a platen temperature of approximately 23°C. The values represent an average of four individual polishing experiments................................................... 159
Table 3.5: Derived effective pressure values for STI polishes at a platen temperature of approximately 35°C. The values represent an average of four individual polishing experiments................................................... 160
Table 3.6: Derived effective pressure values for STI polishes at a platen temperature of approximately 45°C. The values represent an average of four individual polishing experiments................................................... 160
Table 4.1: Statistical regression results for removal rate. Results are listed in ascending order, with the most significance results appearing at the top of the list ........................................................................................ 181
Table 4.2: Statistical regression results for COF. Results are listed in ascending order, with the most significance results appearing at the top of the list... 197
Table 5.1: Modeling parameters extracted in the thermal studies from Sandia National Laboratory study. (*) denotes a parameter whose value was assumed rather than extracted. Two sets of parameters are reported for the thermal oxide data from S&H extracted using eight randomly selected points and values extracted using all of the points....................... 278
Table 5.2: Modeling parameters extracted for the flash heating removal rate model for the results from the Freudenberg pad study .............................. 297
Table 5.3: RMS errors associated with experimental data and theoretical results obtained from several removal rate models. Errors values represent an average of each model against experimental data for a single polishing condition at all platen set point temperatures .................. 298
Table 5.4: Flash heating model fitting parameters for select cases of the Freudenberg pad study with the inclusion of COF. This table also includes a side by side comparison of the relative predictive error associated with the model when including and not including COF........... 302
Table 6.1: Oxide and nitride pattern density statistics for the STI patterned wafers used in this study............................................................................ 331
24
LIST OF TABLES - Continued Table 6.2: Trench oxide thickness after timed polishing................................................ 335 Table 6.3: Window parameters for EPD of STI patterned wafer Sets A through D....... 336 Table 6.4: Motor current endpoint results for STI patterned wafer Sets A through D... 341
25
ABSTRACT
This dissertation presents a series of studies that describe the impacts of, among other
things, temperature and kinematics on inter-level dielectric (ILD) and metal chemical
mechanical planarization (CMP) processes. The performance of CMP is often evaluated
in terms of removal rate, uniformity, planarization length, step height, defects and
resulting topography such as erosion and dishing. The assessment of these parameters is
significantly dependent on the selection of tool and consumable set (polishing pad or
slurry type), as well as the kinematics involved in the process. Variations in pressure,
sliding velocity, temperature and slurry flow rate are just a few of the dynamic inputs that
can affect polishing performance. The studies presented in this dissertation focus on some
of these external parameters and how they influence the mechanisms involved with the
CMP process and their overall outcome on performance.
Studies presented in this dissertation include topics such as the effects wafer-ring
configurations and wafer geometries on the applied wafer pressure distribution across a
wafer surface. In addition to this, another study related to understanding applied wafer
pressure investigated the estimation of the effective (envelop) pressure for patterned
shallow trench isolation (STI) wafers during CMP. When considering the regularity of
issues such as changing wafer geometries and wafer feature patterns, these two studies
provided significant insight on the potential issues that could arise during CMP when
dealing with such events, as well as potential solutions for controlling such events.
26
Another study in this dissertation investigated the effects of polishing pad type on
dielectric CMP performance. Polishing pads varied in thickness and grooving, and tests
were done to characterize the tribological and thermal behavior of the pads under a wide
range of p × V and slurry flow rate conditions. Of key importance in this study was
observing any combined effects between changes in platen set point temperature and pad
type on ILD removal rate.
The greatest contribution to this dissertation involved studies related to the role of
temperature in CMP. These studies implemented variable platen set point temperatures to
further understand the thermal effects on parameters such as removal rate and coefficient
of friction (COF). As a result of these studies, a new removal rate model based on flash
heating was developed to describe observed non-linear trends in removal rate. The
application of this model has shown great utility in removal rate prediction when
compared to prior models.
27
CHAPTER 1 – INTRODUCTION
1.1 Introduction to Chemical Mechanical Planarization
Originally introduced by the Monsanto Company in 1962, commercial chemical
mechanical planarization (CMP) began as a process used to prepare single-crystalline
silicon wafers for the fabrication of integrated circuits (IC) (Walsh et al., 1965; McIntosh
et al., 1980). Monsanto’s groundwork for achieving a planar and scratch-free wafer
surface has since been improved and expanded upon to meet the demands required by the
rapid evolution of the IC device. In fact within the past 40 years, advancements in IC
technology have driven the number of components present on a single chip by nearly five
orders of magnitude (see Fig. 1.1, Chang et al., 1996). Based on this evidence of growth
and the current production of ultra large scale integrated (ULSI) circuit devices, it should
be established that the performance requirements imposed on the CMP process have
dramatically changed since the early 1960’s. With the accelerating growth of IC
technology and the growing expectations placed on CMP, the need for understanding,
predicting and explaining the science of CMP has become more apparent.
In view of all the current applications of CMP in ULSI technology, the primary
purpose of the CMP process remains the same since its inception: to yield a planar and
defect free (i.e., scratches, dishing, erosion, etc.) die-level and wafer-level surface (i.e.,
local and global scale respectively), using the combined action of chemistry and
mechanics (i.e., applied pressures and sliding velocity). In attaining this goal, CMP in
28
turn enables the fabrication of multi-level ULSI devices in two respects: (1) Providing a
suitable surface for patterning steps through the reduction of local and global level
topography. (2) Providing an anisotropic approach of removing deposited inter-level
metals in order to yield optimal structural and resistive uniformity among every
individual inlaid interconnect structure (this is also known as a damascene process).
With a rapidly growing IC field and a perpetual demand for CMP in IC fabrication, it
is of critical importance that the fundamental aspects of CMP be investigated. Seeking
out better alternatives to current processes could potentially improve process performance
and reduce both the process costs and the potential impact on human health and the
environment.
29
1.E+00
1.E+01
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pone
nts
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hip
SSI
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ULSI
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1
(b) Bipolar transistor
(c) MESFET(d) MODFET
(s) MOSFET (DRAM)
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1 G
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MSI
LSI
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109
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102
101
1
(b) Bipolar transistor
(c) MESFET(d) MODFET
(b) Bipolar transistor
(c) MESFET(d) MODFET
(s) MOSFET (DRAM)
1 K
4 K
16 K64 K
256 K
1 M
4 M
256 M
64 M
16 M
1 G
(s) MOSFET (DRAM)
1 K
4 K4 K
16 K64 K64 K
256 K256 K
1 M1 M
4 M4 M
256 M256 M
64 M64 M
16 M16 M
1 G
Figure 1.1: Growth of the number of components per IC chip (Chang et al., 1996)
30
1.2 History of Polishing
Historically, the development of CMP has evolved from two primary practices:
grinding, which was first employed during the Neolithic period, and lapping, which was
first used during the 10th century. Over time, it was the combination and refinement of
these technologies which brought about the current adaptation known as CMP.
As mentioned above, the origins of grinding stem back to the Neolithic period (8000
– 3000 B.C.E.) of human evolution (http://www.britannica.com, 2004). Also known as
the New Stone Age, this period marked the final stage of the cultural and technological
development among prehistoric humans. During this time, prehistoric humans developed
stone tools and weapons with a matte finish by grinding a stone work-piece against other
materials of comparable strength in a deliberate fashion. This method was a significant
advancement compared to the Paleolithic era (approximately 2 million years ago), when
early humans used fortuitous stone chipping techniques to create tools and weapons. The
invention of grinding allowed for more capable tools and weapons for cutting and
hunting. Despite this, the grinding process still lacked the ability to generate precise
work-piece geometries (approximately 5 µm in surface non-uniformity).
With the advent of grinding established thousands of years ago, refinement of the
process progressed through the years using work-piece materials such as copper, bronze
and other metals. It was during this time that grinding techniques were improved to
provide better accuracies to forms and surface finishes. This was primarily done by an
assessment of various grinding materials and ultimately resulted in a process that could
31
yield a crude mirror-like finish with greater control on the final geometry of the work-
piece (http://www.britannica.com, 2004).
Approaching the early 10th century, the emerging interest and value of precious
jewels created a greater need for a more precise grinding technique. Up until this point,
the application of the previous techniques would result in a significant loss of precious
material and yield an unaesthetic finish. Due to the sheer value of jewels, the need for a
more refined process led towards the second generation of polishing known as lapping.
Lapping describes the process of generating a desired surface geometry by the action of
sliding a work-piece material (i.e.,, a jewel) against a lap (typically cast iron or brass).
However, the distinguishing characteristic lapping has over prior processes is the
inclusion of an aqueous solution of abrasive particles (i.e., slurry) at the contact interface
of the work-piece and lap (Marienescu et al., 2000).
The addition of small particles in the lapping process allowed for finer precision
when conditioning the surface of a work-piece. These small abrasive particles usually
came in the form of sand combined with water or mud-like slurries and were typically 5
to 20 µm in size (Marienescu et al., 2000; Parks, 1990). Similar to a current wood
sanding process, lapping employs abrasive particles by creating small cracks (up to 20
µm in depth) on the work-piece surface through the action of applying a pressure and
sliding the work-piece across the lap (Parks, 1990). The rolling action of the particles
across the material surface gradually chips away at the work-piece surface in a controlled
fashion, thereby enabling users of the process to form desired geometries with accuracy.
32
To indicate the extreme value of the lapping process, it should be noted that since the
introduction of the process during the 10th century it is still considered a common
practice to this day. In addition to its importance of utility, the lapping process also
provided the foundation for more advanced glass polishing techniques that arose around
the end of the 13th century.
As society approached the dawn of the Renaissance (13th century A.D.), a growing
popularity in religion and advances in general science and cultural arts heeded the need
for optical lenses. Although credit cannot be given to a particular individual for the
invention of the optical lens, it is suspected, through dated paintings, that optical lenses
first appeared in a painting by Tomaso de Modena around the year 1360 and it was not
until the late-1300’s that optical lenses for eyeglasses were considered commonplace
(Twyman, 1955).
The invaluable utility of eyeglasses during this time brought about an ‘unseen’ level
of human dependence on the invention. It can be safely said that the extent to which
society was dependent on eyeglasses presented the first true case in which the grinding/
lapping process found a required need for a suitable final product as demanded by society
at the time. In general, the finished optical lens called for finer precision in geometric
form (less than 5 µm in surface non-uniformity) and a relatively scratch-free surface. If
these criteria were not met, then the functionality of the optical lens would be considered
inadequate by the user.
As a result of these constraints, the lapping technique could not be solely utilized in
creating the final product, but rather to simply wear the starting material down to its near
33
perfect form. Beyond this however, lapping left undesirable finishes on the lens surface
and needed to be replaced by a more precise process. This led the way for glass polishing.
Compared to grinding, the distinguishing factor of polishing, which permitted finer
geometric precision and a relatively smooth surface finish, was the use of softer lapping
materials. Materials such as wood, cloth and leather allowed for less intrusive scratches
on the work piece surface as a result of a different interfacial contact mechanism between
the lapping material, abrasive particles and work-piece. In lapping, abrasive particles are
pressed against two rigid materials and roll along the surfaces when a sliding motion is
induced. Generally, this process would generate crude subsurface scratch depths of up to
20 µm (Parks, 1990). In polishing however, the abrasive particles are pressed against a
rigid material (i.e., the work-piece) and a soft lapping material. When a sliding motion is
induced, the particles are elastically retained by the soft lapping material and slide across
the work-piece surface creating submicron scratch depths. This action of creating
innumerable submicron scratch depths allows for a finer and more controllable process,
thereby achieving the goals demanded of glass polishing.
Since its application on optical lenses, the polishing process has essentially remained
the same to this day. Over the past 700 years, innovations in technology have brought
about a spanning need for various polishing applications. Depending on the type of
material being polished and its application in science or society, the requirements
expected by consumers have become more rigorous and have driven polishing to
unforeseen levels of accuracy and precision. It has been the driving need for
understanding the underlying science of polishing that has brought the technology to its
34
current status of a chemical and mechanical process. Prior to the past 45 years, polishing
was predominately considered a mechanical process, however with more recent works by
Cook and Tomozawa, the interactions involved in polishing (specifically glass) have
shown that the role of chemistry is far more significant than once thought (Cook, 1990;
Tomozawa, 1997). The coupled progression of understanding the mechanical and, as of
the past 45 years, the chemical facets of the polishing process, have evolved to make
CMP what it is today.
1.3 State-of-the-art CMP Processing and its Applications in Semiconductor Fabrication
Since the introduction of the first IC device in 1959, the semiconductor industry has
grown to nearly $679.7 billion in global sales (as of 1993), with the United States
comprising 40 percent of the market (Chang et al., 1996; Plummer et al., 2000). Rapid
development of IC technology has been the primary driver for the remarkable economic
growth of the industry. Fundamentally, ICs (i.e., chips) are electronic devices that consist
of many individual components (i.e., transistor, resistor, capacitor, etc.) that are
fabricated on a common substrate (semiconductor) and wired together to perform a
specific function. From approximately ten components in 1959, the number of
components per IC has nearly doubled every two years for the last 40 years. Also known
as Moore’s law, it was Gordon Moore who pointed out in 1965 that IC device complexity
would double every generation, where a generation would constitute about 18 months.
35
Moore also noted that the cost associated with designing each device generation would
rise by the same approximate rate (Plummer et al., 2000).
Until the 1970’s the parallel trend in IC cost and complexity was a reality, however
the introduction of computer aided design (CAD) programs enabled designers to continue
in the trend of creating complex devices but at a margin of the expected cost. This stage
in IC development also marked a significant revolution with respect to the development
of fabrication tools. Under the forecast set forth by Moore’s law, IC manufacturers were
faced with the reality of having to reduce device feature sizes to meet expectations. In
fact, since the introduction of the medium scale integrated (MSI) circuit in the 1960’s, the
rate of reduction in the minimum device feature length has been 13 percent annually
(Chang et al., 1996; Plummer et al., 2000). As seen from Fig. 1.1, the growth in
components per device has brought IC technology to its current state-of-the-art ULSI
circuit device, which can have up to 109 components per chip.
Smart and efficient device design has not only decreased the relative value of each
chip generation (see Fig. 1.2), but it has concurrently done so by enhancing the
performance of each generation. As it is known, decreases in feature length reduce the
overall device size, thereby increasing the packing density and reducing the overall cost
of function. Furthermore, decreases in device size (feature length) have increased device
speeds and decreased power consumption. As the industry strives towards reaching new
levels of design complexity and feature lengths of nearly 0.13 µm, the tool and process
capabilities that will be required for such fabrication will require extremely high degrees
of repeatability, uniformity and yield (ITRS roadmap, 2003). One such process is CMP.
36
1E-10
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Electron tube Semiconductor Devices
Figure 1.2: Size and price reduction of electronic components (Chang et al., 1996)
37
As stated by the 2003 edition of the ITRS, “Increasingly, planarization has become an
enabling step for interconnect technology. As materials and structures become less
conventional and demands on planarization tolerances become more exacting,
planarization processes themselves become more closely coupled to the choice of
integration scheme. CMP and near alternatives remain the leading planarization
technologies for current and future manufacturing.” From the above quote, it is clear that
the role of CMP as the leading planarization technology will continue to be critical for IC
fabrication.
In general, the IC fabrication process can involve almost 200 individual steps, each
step building upon a previous step. The precision and accuracy involved in each step
must result in a well-controlled structure for following steps. The above description is
most suited to describe the role of CMP. As seen in Fig. 1.3, following any deposition
step (inter-level dielectric, ILD, metal or metal barrier) during fabrication, CMP must be
employed to eliminate any topography over which the next layer must be processed.
The elimination of topography during CMP has several benefits which are as follows:
(1) higher subsequent photolithography yields and (2) a reduction of inhomogeneous
metallization layer thicknesses. The former is associated with creating a planar surface to
eliminate possible focusing and image transfer issues related to the photolithography step
of fabrication. This is a common expectation after an ILD deposition step. With the drive
towards device size minimization, the smaller wavelength lights required to create
submicron feature patterns has brought more attention to this aspect of planarization and
has set more stringent limits on surface planarity.
38
Si
SiO2
Si Si
(a) Non-planarized Surface, time = t0 (b) Smoothed Surface, time = t1
(c) Locally Planarized Surface, time = t2 (d) Globally Planarized Surface, time = t3
Si
SiO2
Si
SiO2
Si
SiO2
SiSi SiSi
(a) Non-planarized Surface, time = t0 (b) Smoothed Surface, time = t1
(c) Locally Planarized Surface, time = t2 (d) Globally Planarized Surface, time = t3
Si
SiO2
Si
SiO2
Figure 1.3: Step-by-step schematic of an ideal shallow trench isolation (STI) silicon dioxide CMP process where t0 < t1 < t2 < t3
Figure 1.4: Cross sectional view of a typical interconnect line (not to scale)
d
l
t
ILD
Metal
xy
z
d
l
t
ILD
Metal
xy
zx
y
z
39
The latter benefit pertains to the dimensions of the many inlaid metal lines following
metal polishing. Based on the general equation used to determine the speed of an
interconnect, Eqn. (1.1), the RC time delay, τ, appears as a function of several
dimensional parameters associated with the inlaid metal interconnect lines.
dtl⋅
⋅⋅=2
ερτ (1.1)
In the above equation ρ and ε are the intrinsic resistivity and permittivity of the metal
respectively, l is the metal line length, t is the adjacent dielectric thickness and d is the
metal line thickness (see Fig 1.4). When one considers the thousands of metal lines on
single IC layer, the importance of planarizing these features into uniform structures is of
extreme importance for product performance. As seen from Eqn. (1.1), if adequate
planarization is not achieved (i.e. dimensional variation of interconnect structure), the
possibility of having individual interconnects with variable RC time delays (likely result
from over polishing) or current leakage issues (likely result from under polishing) would
be catastrophic.
Aside from the above benefits, additional benefits from CMP include (Zantye et al.,
2004):
• Reduction in step coverage issues
• Higher dry etch yields
• Reduction of prior level defects
• Elimination of undesired contacts and electro-migration effects
• Ability to limit the stacking height of metallization layers
40
As mentioned before, the conventional CMP process was introduced by the Monsanto
Company in 1962 to planarize raw silicon wafers for IC fabrication following the
intrusive and defect causing sawing process for creating a wafer. Monsanto used this
process on silicon substrates as well as other semiconductor materials (i.e., germanium,
sapphire, etc.). The first generation CMP process was suitable for several years, however
as the IC industry approached the late 1960s, the desirable material properties of silicon
propelled the material to become the most favorable for fabrication. By settling on silicon
as a universal base material for IC’s, the industry began a push towards refining the CMP
process for its specific application on silicon.
In 1969 Joseph Regh and a group of engineers from IBM developed and patented a
method for plating and polishing a silicon planar surface (Regh et al., 1969). Unlike the
general approach introduced by Monsanto, Regh et al., established a process solely for
polishing silicon. The key improvement made by Regh et al., was in form of a cupric salt
slurry. Unlike Monsanto’s alkaline-silica based slurry, which proved suitable for a wide
array of semiconductor materials, IBM employed a cupric salt slurry (CuNO3),
exclusively for silicon polishing, and was able to show an improvement of the surface
finish. Specifically, the slurry was customized to reduce defects and surface non-planarity
introduced by preceding etching and deposition steps.
With the development of more complex IC devices during the 1970s and 80s, the
materials and structures used for ICs became less conventional and demands on
planarization tolerances became more challenging. During this time, the CMP process
underwent a series of improvements with respect to the design of tools and consumables
41
(i.e., polishing pads and slurries) (Goetz et al., 1972; Kushibe, 1976; Nelson, 1986;
Chow, 1988). The application of dielectric materials such as deposited silicon dioxide
and silicon nitride promoted the development of high performance slurries.
Advancements in the fabrication process of abrasive silica particles for slurries provided
the option of using colloidal or fumed silica slurries for various dielectric CMP processes.
Similarly, metals such as tungsten (used for plugs) and aluminum (used for metal lines),
introduced several novel slurry chemistries embracing the reactive tendencies of metals.
In 1988, the first commercial CMP tool was introduced by Cybeq Corporation in Japan
and spawned a drive for other companies to enter this soon-to-be growing market.
Moving towards the 21st century, IC devices became more commonplace in
workplaces and homes. The extent of human dependence on computers and the speed and
reliability of processors drove a demand-based market for better chips. This initiated two
primary shifts in IC fabrication design and consequently CMP. The first was the
continuing strive for feature size shrinkage. In order for a more efficient use of chip
space, shallow trench isolation (STI) technology was developed to replace the previous
local oxidation of silicon (LOCOS) technology. As seen in Fig. 1.5, the STI design
presented a more compact alternative to the preceding LOCOS design. Furthermore, STI
technology had other advantages over LOCOS such as low junction capacitance, near
zero-field encroachment and exceptional latch-up immunity (Gan, 2000). The general
structure and nature of materials used in STI technology generated several complexities
for CMP such as selectivity issues (i.e. oxide vs. nitride removal rates), nitride erosion
and trench oxide dishing. These problems are generally associated to variations in wafer
42
pattern density and the overall material properties (i.e., Young’s Modulus) needed for
STI fabrication. Despite this however, CMP technology progressed forward with several
potential solutions. These came in the form of smart consumable designs such as non-
porous pad applications, selective slurry chemistries and endpoint technologies.
The second shift in IC fabrication design brought CMP to the current state-of-the-art.
In order to keep up with demands for performance speeds and reduced energy
consumption, the IC industry needed an alternative to aluminum as the sole interconnect
material. The intrinsic properties of aluminum make it such that it cannot handle high
power density applications. This is primarily due to aluminum’s low resistance to
electromigration, or the process of metal atoms diffusing (metal thinning) as a result of
bombarding electrons carried by transferred currents (http://semiconductorglossary.com,
2005). During the late 1990s, copper was selected as the most suitable alternatives to
aluminum. Compared to aluminum, copper was shown to possess a high resistance to
electromigration effects and low electrical resistivity. In addition to these desired
properties the implementation of copper also meant a reduction in fabrication cost. This
was due to the fact that copper techniques required fewer (approximately 25 percent)
processing steps (Singer, 1998).
Coupled with the higher device density, the copper CMP process presented several
new challenges. These were, and still are, related to polishing selectivity and associated
issues such as dishing and erosion. To date, several plausible solutions have been
developed including novel pad designs and slurry chemistries, as well as low-stress and
multi-step polishing techniques. Although the CMP process has shown exceptional
43
robustness and reliability, it is an ever-growing technology that continues to face many
challenges. The continuing drive towards improving IC technology and performance will
bring forth more complex and delicate materials for fabrication, thereby heeding the
improvement of CMP technology. Along these same lines, new technologies such as
micro-electro mechanical systems (MEMS) bring about new and diverse issues for CMP.
Adapting CMP to a variety of materials, designs, structures, and processes will continue
the effort of refining and improving the process towards the goal of meeting future issues.
Figure 1.5: Side profile (with upper layers removed for simplicity) of typical device isolation technologies. (a) shallow trench isolation (STI) and (b) local oxidation of silicon (LOCOS)
Si(a)
Si(b)
Silicon Dioxide Silicon Dioxide
SiSi(a)
Si(b)
Silicon Dioxide Silicon Dioxide
44
1.4 Equipment and Consumable Design Considerations in CMP
As mentioned earlier, the CMP process occurs as a wafer surface is moved across a
polishing pad with an applied pressure, in the presence of slurry. The polishing pad,
usually polyurethane based, provides a surface with small rough points known as
asperities. These asperities make contact with the wafer to sweep away material on the
surface of the wafer. The slurry imparts abrasive particles and an appropriate chemical
environment for a well-controlled removal mechanism. As the polishing process ensues,
the mechanical contact by the wafer on the polishing pad wears away existing asperities,
thereby requiring the regeneration of a rough, asperity rich pad surface. An abrasion
process known as diamond conditioning is employed to restore asperities on the pad
surface. Figure 1.6 shows a general schematic of the CMP process for a conventional
rotary tool.
As described in the previous section, a majority of advances in CMP technology have
come in the form of the consumables (pads and slurries) and tools. The subsequent
sections will discuss some general design considerations for polishing pads, slurries,
CMP tools, and associated tool equipment.
45
Rotating Platen
SlurryRotating Wafer
Polishing Pad
Diamond Conditioner
Rotating Platen
SlurryRotating Wafer
Polishing Pad
Diamond Conditioner
Figure 1.6: Side-view schematic of the CMP process for a conventional rotary polisher (not to scale)
46
1.4.1 Pads
There are several types of polishing pads used for ILD and metal CMP.
Considerations in pad design are geared towards meeting the goals of providing optimal
polishing results, while efficiently utilizing slurry and maintaining a long pad lifetime.
Polishing pads can vary in material type, porosity, pad thickness, grooving type, density
and hardness. The conventional industrial CMP process occurs in two stages, each
performed on an exclusive polishing platen. The first is a primary polish that removes the
majority of the surface material. This process is usually done with a urethane-based pad,
which is harder and more capable of generating polished surfaces with longer ranges of
planarization. The second polish is intended for buffing and is usually done on soft,
poromeric pads. The rest of this section will focus on the harder urethane based pads used
for bulk material removal.
When selecting a base material for pads one must consider several mechanical and
chemical requirements. Mechanical properties include a high strength to resist tearing
during polishing, suitable levels of hardness based on the material being polishing and an
adequate abrasion resistance to avoid excessive pad wear. Chemically, one desires a
material that is resistive to aggressive slurry chemistries and is sufficiently hydrophilic.
Based on these criteria, the polymeric form of urethane is considered to be the best
material for CMP (Oliver, 2004). As seen in Fig. 1.7, polyurethane is formed by the
reaction of polyol and isocyanate (either the di- or poly-functional group of isocyanate)
(Lenz, 1967).
47
Figure 1.7: Chemical reaction for the formation of polyurethane (http://islnotes.cps.msu.edu)
The molecular structures of polyurethane can vary from rigid cross-linked polymers
to linear elastomers. This variation in morphology gives polyurethane the unique feature
of having ‘soft’ and ‘hard’ segments. Soft segments are comprised of high molecular
weight diol chains of the urethane and comprise of regions with increased flexibility,
toughness and resistance to wear. Hard segments are cross-linked portions of the pad and
are regions of the pad with increased strength and stiffness. The relative amount of these
segments is a significant determinant of the controlling properties of the pad and can
somewhat be controlled by the annealing conditions of the polymer reaction itself.
Typical CMP pads are comprised of closed pore structures with spherical diameters
ranging between 30 to 50 µm (see Fig. 1.8). On average, the pores take up approximately
one third of the total pad volume and facilitate the transport of slurry to the pad-wafer
interface (Oliver, 2004). The extent of pad porosity also dictates the extent to which
properties such as pad density, pad hardness and pad modulus are effected (the extent of
R = R = R =
48
pad porosity is inversely proportional to the aforementioned properties). Table 1.1 shows
the typical physical properties of the polyurethane based Rohm and Haas IC-1000TM
polishing pad, which has an approximate porosity of 880 ± 120 cells per unit area.
50 um50 um
Figure 1.8: Cross sectional SEM image of IC-1000TM polyurethane based polishing pad
Polishing pads have also been designed to be non-porous. Non-porous pads are not
commonly used in industrial applications due to the high extent of material hardness and
a poor response to diamond conditioning, however in cases where high removal rates and
high global planarization results are required non-porous pads may be utilized (i.e., first
level STI trench oxide CMP). One example of a non-porous pad is the JSR water soluble
particle (WSP) pad. This pad is non-porous in nature but contains embedded, micron size,
particles that dissolve upon contact with water. Through slight agitation of the pad
49
surface with diamond conditioning, the WSP are exposed and dissolve away to create
voids on the surface of the pad. This in turn creates pores on the pad which resemble
those of traditional polyurethane based CMP pads. The amount of WSP embedded into
the pad can vary from none to ‘high’ based on the requirements of the CMP application.
Furthermore, the polymeric composition of the pad can also vary such that the pad can
have soft or hard material properties. CMP characteristics of the JSR WSP pads are
detailed elsewhere (Charns, 2003).
Table 1.1: Characteristic physical properties of IC-1000TM polyurethane based polishing pad (Oliver, 2004)
The thickness of a polishing pad determines the overall properties of a pad. Based on
the Machinery’s Handbook, pad stiffness is proportional to the product of pad Young’s
modulus and the pad thickness to the third power (McCauley et al., 2004). This design
consideration proves to be important when one considers that pad stiffness affects
Property ValueDensity (g/cm3) 0.748 ± 0.051Hardness (Shore D) 52.2 ± 2.5Shear Strength (MPa) 51.2 ± 4.1Proportional Limit (MPa) 9.1 ± 1.3Tensile Strength (MPa) 21.6 ± 2.8Elongation to Break (%) 175.0 ± 20.0Storage Modulus (MPa) 310.0 ± 40.0Loss Modulus (MPa) 28.0 ± 4.5Tan Delta 0.090 ± 0.005
50
parameters such as wafer- and die-level planarity. Conventional CMP pads such as the
IC-1000TM are 1.3 mm thick, as received, however when one considers the progressive
wear of the pad from the impacts of polishing and diamond conditioning, the resulting
decrease in pad stiffness corresponds to slight changes in polishing parameters such as
removal rate and uniformity. This design consideration is the focus a study done as part
of this dissertation and will be discussed in a later chapter.
Groove design is another significant consideration regarding polishing pads. Pad
grooves are regarded as macro-features, whereas pad asperities, pores and furrows
created by diamond conditioning are considered micro-features. Grooves provide a
channel for efficient and uniform slurry distribution across the pad surface and the pad-
wafer interface (Sohn et al., 2000), as well as providing uniform pressure distribution
during CMP. Furthermore, grooves prevent hydroplaning at the pad-wafer interface by
creating disruptions in the continuous layer of fluid, which could exist when using a flat
pad. Finally, pad grooves provide an effective channel for the removal of entrained debris
and the subsequent replacement with fresh slurry. Figure 1.9 shows the most typical pad
groove types used in industry to date. The selection of a pad groove type depends on the
material being polished, tool type and slurry type being used.
On a final note, many industrial CMP processes implement the use of softer base pads
in order to improve polishing uniformity. These cushion-like sub-pads enable better
contact between the pad and wafer through improved pad flexibility. As seen in Fig. 1.10,
the polymeric, foam-type, base is much different in structure when compared to the
harder top layer. The improved flexibility encountered by the wafer on the pad has shown
51
to improve wafer-level uniformity at the cost of planarity, however industrially it has
proven enough value for its implementation.
Figure 1.9: Top view of various polishing pad groove types used in CMP
Figure 1.10: Cross sectional SEM image of IC1400TM polyurethane based polishing pad (top) with sub pad (bottom)
100 µm
Top pad
Sub pad
100 µm100 µm
Top pad
Sub pad
(a) Flat pad (b) Perforated pad (c) XY pad (d) K-groove (concentric) pad
(e) Logarithmic spiral positive pad
(f) Leminscate(a) Flat pad (b) Perforated pad (c) XY pad (d) K-groove (concentric) pad
(e) Logarithmic spiral positive pad
(f) Leminscate
52
1.4.2 Slurries
Slurry is the primary agent in the removal of ILD and metal during CMP.
Specifically, silicon dioxide is polished when an abrasive particle from the slurry is
forced against the wafer surface by an asperity tip of the pad. Although the exact
mechanism involved in the removal of the material is not exactly understood, several
models have been proposed to describe and predict this event. These will be discussed in
a later chapter.
Slurry that is applied to ILD CMP is an aqueous solution of metal oxide abrasive
particles, which can range from 10 nm to 200 nm in mean diameter. Particle size and type
are only a few of the design considerations regarding polishing slurries. Other
considerations include slurry pH, viscosity, particle surface charge and solids content.
There are two principal components of slurry, which simultaneously act in the removal of
material: (1) the abrasive particle and (2) the solution. As described above, the abrasive
particle impacts the surface of the wafer and abrades the chemically treated surface of the
wafer material, thereby exposing a new fragment of material for chemical attack.
Depending on the material being polished, the abrasive particle can play different roles.
In ILD CMP, the removal process requires both chemical activity from the abrasive
particle, as well as mechanical abrasion. However, in metal CMP, it is believed that
chemical activity is not required from the abrasive particle, only mechanical abrasion is
required (Oliver, 2004).
53
The solution (chemistry and pH) provides chemical agents that attack the polished
surface and imparts an electrostatic balance for adequate abrasive particle suspension.
Mechanically speaking, the solution provides a lubricating layer at the pad-wafer
interface, controls thermal rises resulting from frictional interactions and aids in the
transport of debris and waste.
Focusing on the removal mechanism of silicon dioxide during CMP, the most
common reaction mechanism used to describe the process was postulated by L.M. Cook
(Cook, 1990). Equation (1.2) shows the generalized reaction between the siloxane bonds
on the surface of a silicon dioxide wafer and water as they would occur during CMP.
( ) ( ) ( )41222 2 OHSiSiOOHSiO xx +↔+ − (1.2)
From the above equation it is apparent that water plays a critical role in the removal
process of silicon dioxide. When polishing a blanket ILD wafer in an aqueous
environment, the oxide surface exhibits a termination arrangement as shown in Fig.
1.11(a). The reason in which water becomes a critical player in this process comes from
the fact that water molecules continuously cover and diffuse into the oxide, thereby
weakening the oxide surface structure in a hydrolyzing process. Furthermore, as this
hydrolyzing process continues, the pH of the local aqueous environment increases with
the increasing formation of hydroxide ions at the surface. It is then suspected that the
increase in hydroxide concentration further weakens the oxide structure through further
diffusion and eventually enables the silica slurry particles to form hydrogen bonds with
the surface of the wafer (see Fig. 1.11(b)). At this point in the removal mechanism, the
slurry particle forms a direct Si-O-Si bond with the wafer surface by releasing a water
54
molecule (see Fig. 1.11(c)). Finally, a fragment of wafer surface is removed by way of
the molecular bond with the slurry particle and the subsequent mechanical removal of
that particle from the pad-wafer interface (see Fig. 1.11(d)).
Figure 1.11: Schematic of a purposed removal mechanism for silicon dioxide during CMP (Chang et al., 1996)
(a) Aqueous silicon dioxide surface
Si Si Si Si Si Si Si Si
O O O O O O O O
H H H H H H H H
SilicaO
H H
OSi
H
(b) Hydrogen bond formation between abrasive and wafer surface
Si Si Si Si Si Si Si Si
O O O O O O O O
H H H H H H H H
SilicaO
H H
OSi
H
(c) Si-O bond formed between abrasive and wafer surface. Water molecule is released
Si Si Si Si Si Si Si Si
O O O O O O O
H H H H H H H
SilicaO
H H
O
Si
O
H H
(d) Removal of a surface Si atom via attachment to an abrasive particle
Si Si Si Si Si Si Si
O O O O O O O
H H H H H H H
SilicaO
H H
O
Si
Si
(a) Aqueous silicon dioxide surface
Si Si Si Si Si Si Si SiSi Si Si Si Si Si Si Si
O O O O O O O O
H H H H H H H H
SilicaO
H H
O
H HH H
OSi
H
(b) Hydrogen bond formation between abrasive and wafer surface
Si Si Si Si Si Si Si SiSi Si Si Si Si Si Si Si
O O O O O O O O
H H H H H H H H
SilicaO
H H
O
H HH H
OSi
H
(c) Si-O bond formed between abrasive and wafer surface. Water molecule is released
Si Si Si Si Si Si Si SiSi Si Si Si Si Si Si Si
O O O O O O O
H H H H H H H
SilicaO
H H
O
H HH H
O
Si
O
H H
O
H HH H
(d) Removal of a surface Si atom via attachment to an abrasive particle
Si Si Si Si Si Si Si
O O O O O O O
H H H H H H H
SilicaO
H H
O
H HH H
O
Si
Si
55
Again, the issue of solution pH is of extreme importance in slurry design.
Specifically, as pH increases from approximately 2.2 (point of zero charge) to about 12,
the rate of silicon dioxide dissolution follows proportionally. In fact, at a pH of 12, or
greater, the rate of hydroxide diffusion into the oxide surface weakens the surface
structure to the point that the oxide begins to chemically dissolve into the solution, thus
resulting in an isotropic etch (Oliver, 2004). For this reason, most slurries are designed to
be water-based (slightly above neutral pH and below a pH of 11.5). Further evidence for
this can be seen in the Pourbaix diagram for the Si-H2O system (see. Fig. 1.12). This
diagram enables one to determine voltage potential and pH conditions needed for the
formation of stable and unstable Si-H2O species. Figure 1.12 shows three areas of
stability with four distinct regions of silicon species formation with water: (1) The area of
stability labeled by Si(s), (2) the area of metastability labeled by SiO2(s), and (3) the area
of instability labeled by Si(OH)3O- and Si(OH)2O2-. Since crystalline silica is not being
polished, only the metastable and unstable regions are considered. If one considers a
constant potential (above approximately -1.5 volts) during polishing, it is clearly apparent
that as the solution pH approaches around 11, unstable species of Si-H2O are formed and
dissolved into solution.
To date, the most common materials used as slurry particles are silica, alumina and
ceria. The selection of the abrasive material type has typically come from experiential
CMP results. Depending on the structural design and material being polished, abrasive
types are selected on the basis of the type which has historically shown optimal removal
56
rate and surface defect results. Table 1.2 shows particle properties for the three most
common abrasive types.
Figure 1.12: Pourbaix diagram of a Si-H2O system (Courtesy of S. Raghavan – University of Arizona).
Silica abrasives are most commonly used for ILD CMP applications. Abrasive
particles in silica slurries often come either in a colloidal form or in a fumed form. These
two types of slurries result in different polishing outcomes based on their size and
structure. Figure 1.13 shows scanning electron microscope (SEM) images of each type of
silica particulate. As mentioned earlier, colloidal particles are typically smaller in mean
diameter (approximately 10 to 50 nm) and fumed silica particles are larger due to their
structural formation (approximately 90 to 200 nm). Colloidal particles are made in
solution through the nucleation of sodium silicate in silicic acid and can be described as
57
singular spherical entities, whereas fumed silica particles are made via a combustion
process and are comprised of an aggregate of many nano-sized silica particle chains
(Microelectronics and the Environment, Class notes, 2002). Both types of particles are
amorphous. In general, the primary design consideration regarding these two types of
abrasive types comes in the form of particle size. An increase in mean particle size results
in greater removal rates, thus making fumed silica slurries more desirable for ILD CMP
applications, as long as it does not compromise the defect results following a polish.
Table 1.2: Material properties for common abrasives in slurries (Oliver, 2004). *(Source: S. Raghavan, University of Arizona, Tucson, AZ)
On a final note, when designing a slurry, regardless of particle size or abrasive type, a
great deal of consideration is given to abrasive suspension and shelf-life. Since slurries
are sold in large volumes, the possibility of particle settling and agglomeration during
storage or usage is of critical concern to many users. In the event of particle settling or
agglomeration, the possibility of inconsistent polishing rates or defects such as of surface
micro-scratches arise (Basim et al., 2002). The principal parameter that controls this
aspect of CMP slurry is electrostatic stabilization. Electrostatic stabilization is the
Property Silica Alumina CeriaParticle Structure Amorphous Poly-crystalline Poly-crystallineCrystal Structure Orthorhombic CubicDensity (g/ml) 2.2 - 2.6 3.9 7.1Hardness (Mohs) 6.0 - 7.0 9.0Point of Zero Charge (pH) 2.2 9.0 7.0Isoelectric Point (pH)* 2.0 - 3.0 8.0 - 9.0 6.5 - 7.0
58
application of repulsive electrical fields between abrasive particles to sustain separation
while in solution. Figure 1.14 considers a single particle in an ionic solution (typical of
most CMP slurries). As shown in the figure, the particle will show signs of several
defining layers near its surface. The Stern layer describes the region surrounding the
particle that could incur molecular adsorption with various ionic species in solution. The
shear layer describes the fluid boundary layer surrounding the particle. The electric
double layer describes the net electric field emitted by the particle.
Figure 1.13: SEM images of silica slurry abrasive particulate types. (a) colloidal silica courtesy of Fujimi Corporation and (b) fumed silica courtesy of Degussa Corporation
In order to assess the behavior of a slurry with regards to possible agglomeration
tendencies, many slurry manufacturers and users evaluate zeta potential. By definition,
the zeta potential of a slurry particle is the electrical charge of the particle at the shear
layer surface. Zeta potential is dependent on the particle type and solution pH and can
vary from 0 mV at the point of zero charge (point of zero charge, PZC, is the point where
(a) Colloidal Silica (b) Fumed Silica(a) Colloidal Silica (b) Fumed Silica
59
the charge of a surface changes from a positive value to a negative value) to the true
surface charge of the particle under vacuum conditions.
Figure 1.14: Schematic of the electrostatic layer formation of an abrasive particle in a slurry solution
When using zeta potential to evaluate the stability of a slurry, an increase in the
magnitude of zeta potential from the slurry PZC generally indicates greater particle
dispersion within the slurry system. If the zeta potential of a slurry system approaches the
PZC, there is a tendency for the particles to agglomerate and settle due to prevailing van
Slurry Particle
––
–––
––
–+
+
+
+
++
+
Distance from Particle
Electric Double Layer
Shea
r Lay
er
Ster
n La
yer
Bulk FlowFluid
Boundary Layer
Surf
ace
of S
hear
(zet
a po
tent
ial)
Slurry Particle
––
–––
––
–+
+
+
+
++
+
Distance from Particle
Electric Double Layer
Shea
r Lay
er
Ster
n La
yer
Bulk FlowFluid
Boundary Layer
Surf
ace
of S
hear
(zet
a po
tent
ial)
60
der Waal and ionic forces. Based on this reasoning, it is critical that the selection of
solution pH and particle type be such that a stable, non-agglomerating slurry is applied
during CMP at all times.
1.4.3 Diamond Conditioning Discs
Pad conditioning is critical in creating an asperity rich surface for optimum polishing.
Pad asperities are essential in material removal during CMP. The mechanical contact of
the wafer on the polishing pad during CMP continuously wears away at the surface of a
polishing pad, removing and flattening any existing asperities on the pad surface. In the
event of pad flattening (seen in Fig. 1.15), removal rates dramatically decrease and wafer
level uniformity becomes poor. Pad conditioning enables abrasion of polishing pad
surface to prevent pad flattening and potential clogging of existing pad pores.
Conventional pad conditioning involves contact between the surface of a polishing pad
and a diamond-conditioning disc. Depending on the pad type and application of CMP
(i.e., ILD, metal, STI, etc.), pad conditioning may be done in-situ (during polishing) or
ex-situ (between polishes) and the conditioning settings will vary with respect to disc
rotational speeds, disc pressure and disc sweeping rates. It should be noted that
conditioning settings are also selected in a compromising manner. Although aggressive
conditioning are likely to produce the best polishing results, the impact on the extent of
pad wear is significant and ultimately proves costly. For this reason, conditioning settings
are selected in order to optimize pad life and polishing performance.
61
Figure 1.15: Top view SEM image of IC-1400TM polyurethane based polishing pad with flattening characteristics from a lack of pad conditioning
Effective aggravation of the pad surface is commonly done using an array of fine grit
diamonds embedded on nickel plated or steel discs. There are three levels of design
consideration for diamond-conditioner discs. The first level is the microstructure of the
diamonds, which is commonly described by grit size. Grit size refers to the average size
of the diamond abrasives. As the grit size number increases, the average size of the
abrasives decreases thus becoming finer and finer. Typical diamond conditioning discs
can range in grit sizes from 60 to 200. This grit size values correspond to mean abrasive
diameters of approximately 270 to 66 µm respectively (McCauley et al., 2004). Based on
the grit size system, diamond conditioners with lower grit sizes abrade the surface of a
pad in a more aggressively when compared to the finer abrasives of higher grit size
100 microns100 microns100 microns
62
conditioners. Figure 1.16 shows the variation of polishing pad surface topography when
conditioning with various diamond conditioner grit sizes.
Figure 1.16: SEM images of resulting Freudenberg polishing pad topography (a) as received, (b) following 60-grit pad conditioning, (c) following 100-grit pad conditioning and (d) following 200-grit pad conditioning
The second level of consideration regards the arrangement of the diamonds over the
area of the conditioning disc. Diamonds can be deposited in several forms. Figure 1.17
shows surface topographies of four various diamond deposition types (electroplated,
sintered grid, brazed grid and random grid). Based on the deposition structure of the
50 um
(a) As received pad
50 um
(b) 60-grit conditioner
50 um
(c) 100-grit conditioner50 um
(d) 200-grit conditioner
50 um
(a) As received pad
50 um50 um
(a) As received pad
50 um
(b) 60-grit conditioner
50 um50 um
(b) 60-grit conditioner
50 um
(c) 100-grit conditioner50 um50 um
(c) 100-grit conditioner50 um
(d) 200-grit conditioner50 um50 um
(d) 200-grit conditioner
63
diamonds on the disc, the wear rate of the pad and the abrasion mechanism on the pad
surface will vary in a non-predictive manner.
Figure 1.17: Available diamond deposition structures for pad conditioners. (a) Electroplated, (b) Sintered grid, (c) Brazed grid and (d) Random grid. (Source: Rohm and Haas Electronics)
The final level of consideration concerns the macrostructure of the diamonds on the
disc. Beyond selecting a grit size and deposition structure, the diamond conditioning
discs may have various macro patterns for which the diamonds may be deposited. The
most common of these patterns is a simple mesh pattern (see Fig. 1.18), which is a basic
blanketing of diamonds along the entire area of the metal disc. Other types of patterns
include spiral diamond layouts and honeycombed layouts. Different diamond patterns can
provide better slurry transport at the conditioner-pad interface or provide differing
(a) Electroplated (b) Sintered grid
(c) Brazed grid (d) Random grid
(a) Electroplated (b) Sintered grid
(c) Brazed grid (d) Random grid
64
magnitudes of conditioning contact area (mesh layouts provide the greatest area of
contact).
Figure 1.18: Mesh patterned diamond pad-conditioner (Source: ABT)
Since pad conditioning is as much of a random mechanism at the actual contact
interface as polishing, the evaluation of diamond conditioners is usually marked by their
overall impact on polishing performance and pad wear. When designing diamond
conditioners, the three levels of consideration are generally selected with only a general
conception of the their actual impact on the CMP process. By empirically analyzing
polishing results from conditioners with differing grit sizes, deposition types, pattern
layouts and process settings, one ultimately makes the selection of a conditioner based on
an optimization of pad wear rate, removal rate and wafer-level uniformity.
65
1.4.4 Conventional and Non-conventional CMP Tools
Conventional state-of-the-art CMP equipment evolved from tools used for glass and
less sophisticated semiconductor polishing. Since the first generation of tools around
1984, tools have become more sophisticated with multiple features and process
capabilities. The importance of effectively integrating consumables such as pads, slurries
and conditioners into the design of a polishing tool ultimately determines the overall
performance of a CMP process. Furthermore, designing a CMP tool with the capability of
performing efficient and stable polishing results wafer-to-wafer is critical for effective
high volume IC manufacturing.
To date there have been four primary CMP tool designs. Each tool design is classified
based on the type of kinematics. The most common and original tool design is the rotary
polisher. Non-conventional kinematic tool designs include orbital, carousel, linear,
planetary and elliptical types. Regardless of the tool type, all CMP tools have several
common design requirements. These requirements include the robotics, mechanical drive
system, down force system, thermal management system, pad-conditioning system, slurry
distribution system, wafer carrier system, wafer cleaning system, metrology system,
waste system and overall control system (Oliver, 2004).
Since tools are classified based on their kinematics, tool selection is specifically
dependent on the various performance results achieved by each type of polishing motion.
Because of this, several types of kinematics have been designed with the objective of
being the best at obtaining the same average velocity at every point on the wafer, while
66
limiting the range of velocity across the wafer. A top view schematic of a conventional
rotary polisher seen in Fig. 1.19, shows the complexity in achieving the above goal.
Based on the geometric dimensions of the wafer and pad, one can position the center
point of the wafer a specific distance away from the pad center in order to achieve a
nearly identical pad and wafer rotational velocity along every point across the wafer. A
proof of this can be shown in the following fashion. First, one must assume the rotation
rates for the pad and wafer are Ωp and Ωw respectively, and that both rotate in the same
direction. Then if one places the center of the wafer at x= wc and let rv and ricR wvvv
+=
be vectors to a point under the wafer from the wafer center and pad center respectively.
Then the relative sliding velocity is
rkRkV wpvvvvv
×Ω−×Ω= (1.3)
rkrick wwpvvvvv
×Ω−+×Ω= )( (1.4)
rkjc wpwpvvv
×Ω−Ω+Ω= )( (1.5)
Thus, when Ωp = Ωw, the sliding velocity is jcV wp
vvΩ= everywhere under the wafer
(Borucki, 2004).
Since rotary polishers come in several dimensions, comparisons in rotational
velocities are often incomparable and conceptually more difficult. For this reason
rotational velocities are often converted and described as linear velocities. Equation (1.6)
shows the mathematical conversion of rotational velocity (Ω) to linear velocity (v),
( )sec60min12 ⋅⋅⋅Ω= πpp rv , (1.6)
67
where Ωp is the rotational velocity of the pad in rpm, rp is the distance between the
pad center and wafer center.
Figure 1.19: Top view schematic of pad-wafer geometry for a conventional rotary polisher (Courtesy of Len Borucki)
The other principal differentiator of CMP tool design that will be discussed is the
wafer carrier system. Wafer carrier design is important because an effective carrier
ensures that the wafer remains in place during the polishing process and inter-tool
transfers. In many ways the wafer carrier system is interrelated with the down force
system of many tools because they work together towards applying uniform pressure
across the entire area of the wafer during polishing. This proves difficult when one
considers the rotational, frictional and fluid film interactions that occur during the
process. Furthermore, a non-rigid polishing pad presents a soft surface for the rigid wafer
Pad center
Wafer center
-
-
Pad center
Wafer center
-
-
68
to dig into. As seen from Fig. 1.20, the induced tilting action varies the pressure
distribution, and consequently the removal rate from the leading edge of the wafer to the
trailing edge. This effect is particularly seen along the edge of the wafer and as it will be
discussed later, is shown to be enhanced due to imperfect wafer geometries. In order to
dampen some of these effects, wafer carriers have evolved from rigid backed, fixed plate,
carriers to membrane backed and zone pressure controlled carriers.
Figure 1.20: Side view of wafer carrier head assembly digging into soft polishing pad along leading edge of wafer (not to scale)
Rigid backed carriers are designed with a retaining ring and compressible, poromeric
insert for the wafer. These carriers depend on mechanical means to transmit applied
forces to the wafer. These carrier types exhibit a high extent of pad digging and poor
pressure distribution due to an inability to conform to the intrinsic and varying wafer
CL
Polishing Pad
Applied Wafer Pressure
Carrier Head Assembly
CLCL
Polishing Pad
Applied Wafer Pressure
Carrier Head Assembly
69
geometries. To eliminate these effects, rigid carriers were slowly replaced by flexible
membrane backings. These membranes allowed for pneumatic pressure control
capabilities, thus significantly improving pressure distributions and removal rate
uniformity.
With the ongoing drive towards high IC manufacturing volumes and increasing
polishing requirements, CMP tools are continuously changing in order to provide more
stable, efficient and accurate processes. One essential and arising concern with tool
design has come from increasing wafer sizes. As wafer sizes increase and feature sizes
decrease, overall wafer geometries have a tendency to change considerably and have an
impact on CMP stability.
1.4.5 Wafers
Wafers used in semiconductor manufacturing and CMP are formed from single-
crystalline silicon ingots. Sawed slices from the ingot are finished such that the wafers
are ready for subsequent deposition and processing steps. Wafer diameters can vary
based on the process conditions used for creating the silicon ingots. In the course of IC
development, wafer diameters have gone from 50 mm to 100 mm to 150 mm to 200 mm
to the current 300 mm wafer. In order to promote a high volume manufacturing (HVM)
environment and maintain low production costs, IC companies have long pushed for
larger diameter wafers. This enables more chips to be designed per wafer, thus yielding a
greater throughput.
70
One characteristic of the wafer that is essential for optimal IC fabrication is flatness.
This is aspect of the wafer is particularly critical for lithography and CMP processes.
Wafer warping, or bending, can occur as a result of deposition or thermal annealing.
Variations in the properties of dissimilar deposition materials such as silicon dioxide,
polysilicon or metals can create non-conformal bonding with prior surface layers. This
can cause tensile bending or expansion between the dissimilar materials. This effect is
enhanced when wafers undergo thermal treatments such as annealing. The structural
effects of deposition and annealing cause wafer geometries to take on convex or concave
shapes. Furthermore, such wafer geometries in CMP can be considered catastrophic to
the process. Although wafer carrier systems are designed to compensate for slight
deviations in wafer geometry, they are not capable of handling such dramatic wafer
shapes. As a result, warped wafers can cause excessive pad wear and significant global-
level non-uniformity (commonly at the edge of the wafer).
On a final note, it should be mentioned that despite the push for larger wafer
diameters for IC manufacturing, a major drawback to increasing wafer diameter is its
tendency to warp and bow more easily through processing stages. Although the payoffs
may out number the drawbacks, the demand for larger wafers has placed more
restrictions and design considerations on critical process steps such as CMP. This will be
discussed further in Chapter 3.2.
71
1.4.6 Endpoint Detection Tools
The implementation of a robust in-line monitoring system during CMP presents
significant advantages to development and manufacturing environments. An effective
endpoint detection (EPD) system has the potential of improving yield, increasing
throughput, reducing wafer-to-wafer variability and improving planarity (Hetherington et
al., 2001).
Many forms of EPD have been implemented in CMP. These include thermal, optical,
acoustic, electrochemical, electrical and frictional monitoring. Each method presents an
advantage for a given circuit pattern or type of material being polished. For example, in-
line monitoring for STI CMP has most commonly been achieved by optical methods
(Bakin et al., 1998; Moriyama et al., 1996; Chan et al., 1998; Ushio et al., 1999; Dunton
et al., 1999). In a technique presented by Chan et al., in-situ optical EPD for patterned
wafers was performed using laser interferometry to detect film thicknesses on the front
side of the wafer (Chan et al., 1998). Other such attempts have also been made, however,
patterned wafers present difficulty during optical in-line monitoring due to diffraction
and scattering effects caused by wafer movement over the detector and light source.
Frictional monitoring, or motor current EPD, has recently emerged as a viable method
for endpointing. It is suspected that frictional effects generated by the pattern structures
and various layered materials on the wafer will create distinct and characteristic
responses for determining an appropriate endpoint. One problem typically associated
with motor current detection is poor signal-to-noise ratio due to extraneous frictional
72
effects. These are commonly caused by in-situ conditioning, similarities in the frictional
signals between like materials such as silicon nitride and silicon dioxide (Hetherington et
al., 2001), tool hardware, or other physical defects associated with consumables used in
the process (Lin et al., 1999; Kim et al., 2001; Kim et al., 2003). In order to achieve
effective motor current EPD, a high degree of noise filtration is required (one method of
reducing some of this superfluous noise is by performing polishes ex-situ). It should also
be mentioned that motor current EPD is highly dependent on the set of consumables
being used during CMP. Consequently, endpoint recipes must be matched to a certain
type of pad or slurry.
1.5 Motivation and Goals of Study
The performance of CMP is evaluated in terms of removal rate, uniformity,
planarization length, step height, defects and resulting topography such as erosion and
dishing. The assessment of these parameters is significantly dependent on the selection of
tool and consumable set, as well as the kinematics involved in the process. Variances in
pressure, sliding velocity, temperature and slurry flow rate are just a few of the dynamic
inputs that can affect polishing performance. The following section and sub-sections will
discuss the evaluation parameters used to determine polishing performance and the
dynamic factors that were studied for the fulfillment of this dissertation.
Material removal in CMP is measured in terms of rates. Since early glass polishing it
was apparent that as the applied pressure or rate of motion were increased, more material
73
would be removed in a given time. The first effort towards modeling and predicting
material removal rates was by F. W. Preston in 1927. Preston’s empirical, mechanically-
based removal rate model for plate glass polishing has been the traditional approach and
benchmark for describing the polishing of materials in CMP (Preston, 1927). As seen in
Eqn. (1.7), Preston observed that removal rate (RR) was directly proportional to the
applied pressure (p) and rotational velocity (V) of the substrate.
pVkRR ⋅= (1.7)
Removal rate is a critical factor for determining polishing performance for several
reasons. In a manufacturing setting, high removal rates are desired because it translates
into higher production throughputs. Depending on the structural pattern design on a wafer
and the material polished, removal rates will vary greatly. Selection of process pressures
and velocities are tailored to provide reasonable removal rates without compromising the
other evaluation parameters (i.e., uniformity, defects, etc.). This becomes especially
critical when one considers patterned wafer CMP.
Figure 1.21 shows a side-view schematic and top-view microscope image of the
observed variations in IC pattern design density. As designs are patterned on a wafer,
their structural landscapes will often vary with respect to density. According to the
Preston’s model, it is apparent that areas with low-density features will polish at faster
rates than areas with high-density features. This is simply due to the high local pressure
experienced over low-density areas (pressure is inversely proportional to area). In CMP,
these local variations in pressure and removal rate are evaluated by the parameter of step
height. As seen in Fig. 1.22, step height describes the vertical height of a surface feature
74
from its lowest planar level. As polish time continues, the magnitude in step height
reduction decreases, thereby reaching approximately zero when a nearly planar surface is
achieved. For effective CMP processing, one would desire as much step height reduction
as possible at the end of CMP without excessive over-polish. This parameter is used to
evaluate polishing on a local scale (defined on a micron scale) since most feature patterns
on this scale can be considered similar enough to deem comparable planarization
characteristics.
Figure 1.21: (a) Side view of various levels of pattern design density. (b) Top-view image of high and low density patterned structures
When one approaches global scales (defined on a millimeter scale or on a die level)
feature patterns can change dramatically enough to produce different planarization
characteristics. Furthermore, when one attempts to evaluate polishing performance on the
10 um
Low Density Region
High Density Region
Low Density Medium Density High Density
(a)
(b)10 um
Low Density Region
High Density Region
10 um10 um
Low Density Region
High Density Region
Low Density Medium Density High DensityLow Density Medium Density High Density
(a)
(b)
75
global level, step height measurements become extremely difficult. For this reason,
polishing is evaluated with the parameter of planarization length. By definition,
planarization length is the distance at which all aspects of the CMP process no longer
interact with step height and do not act in specially removing material from raised areas.
A pictorial representation of this can be seen in Fig. 1.23.
Figure 1.22: Step-by-step schematic of step height reduction as a function of time
Step height
Si
SiO2
Step height
Si
Si
Step height
Si
Local Planarity
Step height
Si
SiO2
Step height
Si
Si
Step height
Si
Local Planarity
76
Figure 1.23: Schematic of planarization length used to evaluate polishing performance on a global scale
Planarization length can be determined through direct measurements or modeling.
Direct measurements often involve the use of profilometry techniques and despite
quicker results, it is not considered the method of choice because the required test
structures needed for planarization length characterization are rather large (i.e.,
millimeter scale). For an effective CMP process, one would desire planarization lengths
that approach zero, however most ILD CMP planarization lengths are on the order of 3 to
5-mm (Oliver, 2004).
In order to relate all of the above described evaluation parameters with CMP in a
manufacturing setting, the performance of a polish is usually judged on parameters such
as removal rate, dishing, erosion and defects, since these parameters ultimately affect
production yields and throughput. These factors combine pattern dependencies, material
property dependencies and all facets involved in CMP together. IC design involves
Metal lines
Planarization Length
SiO2
Metal lines
Planarization Length
SiO2
77
structural levels of various patterns, which, as mentioned, can significantly vary in
pattern density over the area of a die (see Fig. 1.24). Above that, IC design also requires
the use of multiple materials that range considerably in terms of their structural properties
(i.e. ILD and metals). In CMP processing, these elements of IC fabrication have a
dramatic effect on the rate of removal during the polish.
Figure 1.24: Cross section of a 6-level IC design (Source: Intel Corporation)
Dishing and erosion occur as the CMP process approaches the clearing and over-
polish stage. Figure 1.25 shows the events of dishing and erosion during the clearing
stage of a damascene process. Dishing, or thinning, occurs from differences in polishing
rates of two exposed materials such as silicon dioxide and copper. During CMP, the
removal rate of ILD is much lower than metal, thereby creating a recession in the amount
Oxide
Copper
Tungsten
Oxide
Copper
Tungsten
78
of metal removed when both materials are present on the polishing surface. By definition,
dishing refers to the amount of material recessed in a local metal feature such as a trench.
Erosion is more dependent on a pattern layout and is defined as the recession of both the
supporting material (ILD) and inlaid material (metal) with respect to the edge of an array
of features. Dishing or erosion are considered catastrophic events and lead to the ultimate
failure of the IC.
Figure 1.25: Side-view schematic of (a) dishing and (b) erosion during clearing or over-polish stage of CMP
Defects may also be ‘show-stoppers’ in IC manufacturing. CMP defects are generated
during polishing in a multitude of ways. Figure 1.26 shows common examples of defects
CopperDishing
SiO2
(a)
SiO2
CopperErosion
(b)
CopperDishing
SiO2
(a)
CopperDishing
SiO2
(a)
SiO2
CopperErosion
(b)SiO2
CopperErosion
(b)
79
that occur as a result of over-polishing, slurry abrasive particle scratching and poor post
polishing cleaning. Defect prevention is a common practice in CMP and maintaining a
stable, agglomeration-free slurry or consistent pad surface are some routes to defect
prevention. Furthermore, some defects may be eliminated following CMP via post
cleaning steps (mega-sonic wet baths or brush scrubbing).
Figure 1.26: Various defect events that occur as a result of CMP (Source: Sandia National Laboratories)
To provide the best polishing performance for the various CMP applications in IC
manufacturing, understanding the effects of various consumable parameters and dynamic
process conditions on the polishing process is essential. The studies done in this
dissertation drive towards the understanding of an array of mechanical, chemical and
consumable variables and their ultimate effect on the CMP of ILD and copper polishing.
The studies were empirical and theoretical in nature and investigated the impacts of wafer
pressure, sliding velocity and temperature on the removal rate and tribological
characteristics of CMP. The results and conclusions acquired from this work can be
considered towards implementation in conventional CMP processing in a manufacturing
(a) Dishing (b) Micro-scratch (c) Residue (d) Killer Particle (e) Pattern Tearout(a) Dishing (b) Micro-scratch (c) Residue (d) Killer Particle (e) Pattern Tearout
80
setting with the goals of providing higher yields, lowering environmental impacts, and
reducing cost of ownership.
1.5.1 Role of Applied Wafer Pressure in CMP
Applied wafer pressure was investigated in two ways. The first was to understand the
effect of wafer-ring configurations and various wafer geometries on the applied wafer
pressure distribution across a wafer surface. Specifically, this aspect of pressure was an
empirical analysis of previously observed, and modeled, applied wafer pressure
distributions that showed unusual rises in pressure along the edge regions of perfectly flat
wafers. The study expanded beyond the empirical verification of this edge pressure
phenomena by showing the potential impacts of altered wafer configurations (wafer-ring
gaps) and geometries on edge pressure. The extension of the study was novel and critical
since wafer geometries are not perfectly flat in industry and often progressively deviate
from flatness due to thermal treatment.
The second aspect of applied wafer pressure that was investigated pertained to the
estimation of the effective (envelop) pressure for patterned STI wafers during CMP. As
was described above, variations in pattern density cause dissimilarities in contact area at
the pad-wafer interface during polishing. In such cases, the areas with lower pattern
densities polish faster than higher pattern density areas, and ultimately have an impact on
step height reduction rates and planarization length. In order to better understand the
effect of patterns on the actual pressure during CMP, tests were done to estimate the
81
actual pressure of patterned wafers during CMP. The results from these analyses would
provide insight towards how much pressure was effectively being applied during a
patterned wafer polish and how much this effective pressure estimate deviated from the
applied wafer pressure set by the CMP tools.
1.5.2 Role of Tool Kinematics and Pad Geometry in CMP
This study focused on the combined effects of applied wafer pressure, sliding velocity
and pad geometry on the removal rate, tribology and observed temperature during ILD
CMP. Polishing tests were done with a variety of Freudenberg polishing pads and
considered the possible impacts of pad thickness and pad grooving on the CMP process.
This study was also comprised of dynamic mechanical and thermo-mechanical analyses
of each pad type and attempted to correlate these results with possible removal rate or
tribological trends.
1.5.3 Role of Temperature in CMP
To date, the role of temperature during CMP has not been a major focus of literature
studies in CMP. As is the case with all lapping, grinding or polishing processes, the
dynamic contact between the work-piece and the lapping surface generate heat as a result
of friction at the interfacial surface. This heat is then absorbed or dissipated by the
82
various components involved in the CMP (i.e., the pad, slurry or wafer). As this process
takes place, the impact of the heat had on the consumables and wafer during CMP are
reflected on the resulting polishing performance. Frictional heat generated during
polishing may hinder or promote the chemical activity at the surface of a wafer, thereby
directly effecting removal rates and selectivity. This is especially important in metal
polishing. Furthermore, this heat may also change the material properties of polishing
pads and the wafer, thus impacting removal rates, pad conditioning, uniformity and
defect levels. For a process that is expected to be as consistent as possible, the
management and understanding of thermal effects during CMP is of extreme importance
to the reliability and performance of the process.
The studies performed in this chapter investigate the impacts of variable process
temperatures on the removal rates and tribology during CMP. In order to mimic the
generation of frictional heat, tests done in these studies deliberately applied controlled
thermal environments during the polishing. Results from the studies attempt to introduce
temperature as a parameter in predicting and modeling removal rate for ILD and metal
polishing. Moreover, these results also provide the groundwork for a more powerful and
novel removal rate model based on the concept of interfacial flash heating.
83
1.5.4 Removal Rate Modeling
Removal rate modeling is critical tool in IC manufacturing. The ability to predict
polishing rates in an accurate fashion enables CMP to progress in a consistent and
efficient manner. Specifically, it may be utilized to explain possible issues that may arise
such as dishing. To date, the precision of removal rate models have certainly had some
room for improvement. Scatter and deviation of empirical data with existing removal rate
models have given rise to more complex models that attempt to predict removal rate via
physical and chemical phenomena.
Since the introduction of plate glass polishing theory by F. W. Preston in 1927,
Preston’s empirical (see Eqn. (1.7)), mechanically-based removal rate equation has been
a traditional approach and benchmark for describing the polishing of materials in CMP
(Preston, 1927). Measured rates that follow this law are called Prestonian while those that
do not are termed non-Prestonian. In many cases, theories have been constructed to
explain observed non-Prestonian behavior.
Much subsequent work has focused around the specific microscopic mechanisms
responsible for material removal in SiO2 polishing. Cook and Tomozawa discussed
diffusion of water into an amorphous SiO2 layer and the sequential dissolution of that
layer under compressive and tensile loading (Cook, 1990; Tomozawa, 1997). Their work
described the dissolution of the surface SiO2 layer via breakage of oxygen and silicon
bonds to form hydroxyl-terminated silicon. This hydrolyzed surface layer is then easily
84
removed by mechanical abrasion by the polyurethane pad and by slurry abrasive
particles.
Despite evidence of a chemical basis for oxide CMP, many modifications of
Preston’s model that are designed to explain non-Prestonian behavior do not explicitly
incorporate a reaction mechanism. For example, Zhang and Busnaina developed a
removal rate model that went beyond previous elastic models by considering both
electrostatic particle adhesion and plastic deformation (Zhang et al., 1998). This model
was novel in that it identified the overall force responsible for removal as a combination
of the externally applied force from the wafer and the Van der Waals force between
slurry particles and the oxide surface. Their removal rate model,
21
)( pVkRR ⋅= (1.8)
has a sublinear square root dependence on p × V. Using copper removal rate data
produced with an alumina-based slurry, Zhang and Busnaina’s model provided an
adequate fit to non-Prestonian behavior.
Tseng and Wang proposed a mechanical model based on the normal and sheer
stresses occurring during CMP (Tseng et al., 1997). The Tseng and Wang model predicts
that the removal rate is
21
65
VpKRR ⋅⋅= . (1.9)
This model is also non-Prestonian and was intended to link fluid motion and material
wear. They provide the following description of material removal: “The abrasive particles
are first being indented into the polished wafer(s) to cause plastic deformation. The
85
residues from the indentation are then carried away by the flowing slurry to complete a
removal cycle.”
A later mechanical model proposed by Zhao and Shi considered rolling and
embedding of slurry particles at the pad-wafer interface (Shi et al., 1998; Zhao et al.,
1999; Zhao et al., 1999). A modified version of the Zhao and Shi model included a
threshold pressure term, pthreshold. An abrasive particle would slide against the wafer
surface and contribute to removal only if the particle were held firmly by the pad.
Embedding would be possible only when the applied pressure, p, is greater than or equal
to the threshold pressure. If p is less than pthreshold, then the abrasive particles in the slurry
roll between the pad and wafer surface and do not remove material. Zhao and Shi’s
model is
<
≥−⋅=
)(0
)()()( 32
32
threshold
thresholdthreshold
pp
ppppVKRR (1.10)
where K(V) a function of the relative velocity. In the above model, the pressure
dependence arises from a mechanical model in which the contact area between an
indenting spherical slurry particle and the wafer surface varies as p2/3. As a consequence
of this model, and specifically because of the threshold pressure, Zhao and Shi were able
to explain why extrapolations of experimental data to zero pressure sometimes produce
negative rates.
The above models all provide different mechanical explanations for observed removal
rate trends, specifically non-Prestonian trends. In an extensive comparison of these
models, Stein and Hetherington showed that each of the models fits experimental
86
removal rate data about equally well for processes that do not involve chemically active
slurries or films (Stein et al., 2002). Although these models have, to some extent, sufficed
in describing non-Prestonian behaviors, it is evident that they do not consider all of the
mechanisms involved in CMP, specifically the energetic and chemical attributes.
Recent attempts at describing removal rates using energy and friction include work by
Homma et al. (Homma et al., 2003). Homma et al. derived a linear relationship between
removal rate and frictional force that describes processes run with nonlinear characteristic
slurries. Equation (1.11) shows the proposed removal rate relationship, which was
deduced from energy conservation laws:
chnpVRR += (1.11)
In the above equation, h is a removal efficiency coefficient, n is a dynamic frictional
coefficient and c is a constant used to generalize the model. The friction coefficient in
this model poses some difficulty in applications because frictional data acquisition has
not become a mainstream technique on existing industrial tools.
In order to include all aspects of CMP, some recent models have combined chemical
and mechanical approaches. Borst, Gill and Gutmann proposed a general two-step
mechanism for surface removal during CMP (Borst et al., 2002). When initially
introduced, the model was intended to describe low-k (i.e., SiLK) removal during
polishing. However, based on similarities with the removal mechanisms of Cook and
Tomozawa, the model was applied to oxide.
As proposed by Borst et al., a two-step mechanism for surface removal rate
(including oxide) can be described by a subset of the Langmuir-Hinshelwood model. As
87
seen in Eqn. (1.12), in the first of two steps n moles of an unspecified reactant R in the
slurry react at rate k1 with the oxide film on the wafer to form a hydrolized layer, S*ox, on
the surface,
*1ox
kox SnRS →+ . (1.12)
The reacted layer is then removed by mechanical abrasion with rate k2,
AbradedS kox →∗ 2 (1.13)
The abraded material is carried away by the slurry and is not redeposited. The local
removal rate in this sequential mechanism is then
2
1
1
1kCk
CkMRR w
+=
ρ, (1.14)
where Mw is the molecular weight of oxide, ρ is the density, and C is the local molar
concentration of reactant. If it is assumed that there is little reactant depletion (i.e., the
slurry flow rate does not create a reactant-limited process), then C is a constant that may
be absorbed into k1. In Eqn. (1.14), the rate of the chemical reaction is then expressed as
k1= Aexp(-E/kT) with C = 1 (A is the Arrhenius pre-exponential factor, E is the apparent
activation energy of the process, k is the Boltzmann constant and T is the process
temperature). Assuming that the mechanical removal rate is proportional to p × V, then
pVck p µ=2 where cp is a constant and µ is the friction coefficient. In the mechanically-
limited extreme, the polish rate is ( ) pVcMRR pw µρ/= and the classical Preston
coefficient is ρ/pwcMk = . In the opposite limit the polish rate is ( ) 1/ kMRR w ρ= .
88
The work presented Chapters 5.4 and 5.5 investigate the non-Prestonian behavior
seen through a series of temperature controlled polishes of blanket thermal silicon
dioxide, thermally annealed PECVD tetraethoxysilane-sourced silicon dioxide (TEOS)
and tungsten wafers. A novel removal rate model based on flash-heating is proposed,
which shows better utility in predicting removal rates for these materials.
1.5.5 Cost of Ownership and Environmental Impacts
It has been established that CMP is an essential and integral process for IC
manufacturing. The continuous development of the process have led to many great
accomplishments, however the advantages brought forth by these improvements have
also led to several drawbacks. The major drawback to CMP has been its high cost of
ownership (COO). COO is defined as the cost of implementing a given process including
costs for equipment, maintenance, materials, operation, etc. (Browne et al., 2002). The
main factors that give CMP a high COO are polishing pads and slurry. Within the CMP
module of a typical IC manufacturer, slurry and pad usage per wafer roughly account for
more than 33 and 16 percent of the total COO (Stavreva et al., 1997). Figure 1.27 shows
the approximate COO breakdown for a typical CMP module.
The unique aspect about CMP is that most attempts at reducing COO have a positive
impact on the environment as well. For example, two primary approaches in reducing
CMP COO are reducing or creating more efficient slurry usage methods, and prolonging
pad life. It is apparent that with these strives comes the obvious reduction in overall
89
waste. Other COO and environmental concerns associated with CMP include water
consumption (Browne et al., 2002). It has been estimated that the CMP process accounts
for as much as one-half of the entire ultra-pure water (UPW) consumption in an IC
factory. Efforts at reducing water costs and consumption are continuously being
attempted via water reclamation and re-use.
A majority of the work done in CMP is motivated by the ultimate goal of creating
smarter and more efficient processes. This means lowering COO and environmental
impacts. Several studies in this dissertation consider the possible impacts on these critical
and relevant issues.
Figure 1.27: COO breakdown for a typical CMP module in an IC manufacturing setting
Equipment16%
Pad22%
Slurry45%
Labor8%
Other9%
90
CHAPTER 2 – EXPERIMENTAL APPARATUS
2.1 Innovative Planarization Laboratory Scaled Polisher
The CMP tool used for polishing experiments at the University of Arizona’s
Innovative Planarization Laboratory (IPL) is a scaled down version of a SpeedFam-IPEC
472 rotary tool. The scaled down version of this tool was originally designed and
fabricated at Tufts University (Coppeta, 1999; Lu, 2001). Figure 2.1 shows this tool and
most of its accessories. The scaled polishing tool uses a Struers Rotopol-35 tabletop
polishing platform with a 12-inch diameter platen.
A drill press is employed as the 4-inch wafer carrier system for the tool. The drill
press provides the ability for the wafer to engage with the surface of the Struers platform
with both rotation and force. A sliding traverse designed with a weighted carriage is
positioned on top of the drill press and enables the application of variable pressures on
the wafer. By adjusting the magnitude of weight and the location of the weights on the
traverse, variable down forces could be passed onto a gimbaled wafer carrier (the carrier
did not have capabilities for independent control of wafer and ring pressures). It should
be noted that the traverse is positioned such that the pivot point is located directly above
the drill press supporting column. This allowed the transfer of force without creating a
moment about the drill press.
Pad diamond conditioning is done using a removable assembly that is mounted over
the Struers polisher using a simple bolt attachment. The conditioner disc has a diameter
91
of 2-inches and is positioned such that it can be spring loaded onto the polishing pad
platform at specific pressures. Applied conditioner pressures were calibrated using
various spring lengths and a Tekscan® pressure mapping sensor. The Tekscan system
will be discussed in further detail in Chapter 3.2.2. Two stepper motors allowed the
conditioning disc to rotate and sweep independently across the pad.
Figure 2.1: Scaled polishing tool at the University of Arizona’s Innovative Planarization Laboratory
TraverseWeighted Carriage
Isolation Table
Drill Press
Polisher
Friction Table
Slurry Delivery
Conditioner
TraverseWeighted Carriage
Isolation Table
Drill Press
Polisher
Friction Table
Slurry Delivery
Conditioner
92
In order to characterize the frictional effects during CMP, the polisher is placed on
top of a friction table consisting of two parallel plates. Figure 2.2 shows a detailed
schematic and image of this design. The bottom plate of the friction table is bolted to an
approximately 400-lbs isolation table to ensure no movement. The top plate has the
ability to move in a single axis of direction (relative to the bottom plate) via two slider
rods positioned between the plates. A strain gauge mounted between the plates measures
the lateral force applied by the top plate on the bottom plate during polishing. This was
done through a calibration relating voltage output and force.
Figure 2.2: (a) Side view schematic and (b) image of sliding friction table design
Having both the normal force (i.e., normal force for a polish is defined by the product
of the applied wafer pressure and the wafer surface area) and lateral force (i.e., shear
force) during a polish, the parameter of coefficient of friction (COF) was quantifiable
using the relationship shown in Eqn. (2.1).
Strain Gauge
Slider
PolisherDiamond Grit Platewith Rotation & Translation
Applied Wafer Pressure
Sliding Friction TableStrain Gauge
(a) (b)
Strain Gauge
Slider
Polisher
Strain Gauge
Slider
Polisher
Strain Gauge
Slider
PolisherDiamond Grit Platewith Rotation & Translation
Applied Wafer Pressure
Sliding Friction TableStrain Gauge
Diamond Grit Platewith Rotation & Translation
Applied Wafer Pressure
Sliding Friction TableStrain Gauge
(a) (b)
93
n
s
FFCOF = (2.1)
In Eqn. (2.1), Fs is the magnitude of the shear force and Fn is the magnitude of the
normal force for a given polish.
2.1.1 Polisher Scaling
As described earlier, the polishing tool seen in Fig. 2.1 is a 1:2 scaled version of a
SpeedFam-IPEC 472 rotary CMP tool. The SpeedFam-IPEC 472 tool was selected as the
basis for the scaled down tool due to its rotary kinematics and its reputation as a stable
and reliable tool in industry. Furthermore, results obtained on a scaled down version of
this tool could be used comparatively for industrial purposes. To scale, or match, the two
polishers appropriately the following parameters were taken into consideration: applied
wafer pressure, platen and wafer sliding velocities, platen and wafer diameters and slurry
flow rate. Table 2.1 shows these scaling parameters and the respective scaling factors
used for each.
The scaling factor used for applied wafer pressure was unity. Since applied wafer
pressure settings on CMP tools already account for difference of wafer contact area (i.e.,
differences in wafer diameter), this implies that an applied wafer pressure setting on an
industrial grade tool is equal to that of IPL’s scaled down tool.
94
Table 2.1: Scaling parameters for 1:2 SpeedFam-IPEC 472 scaled polisher
The scaling factor used to proportion platen and wafer sliding velocities was
Reynolds number, µ
ρ⋅⋅=
vLRe (where L is a characteristic length, v is the sliding
velocity and (ρ/µ) is the kinematic viscosity). In order to use Reynolds number as a
scaling factor between the tools one had to assume that the kinematic slurry viscosity and
fluid film thickness at the pad-wafer interface were identical between the two polishers.
This assumption made it such that conversions in tool velocities only required the simple
conversion shown in Eqn. (1.6) from described in Chapter 1.4.4.
The ratio of platen to wafer diameter was used as the scaling factor for platen and
wafer sizes. Slurry flow rate was scaled using the ratio of slurry flow rate to the platen
surface area.
Parameter Scaling Factor Speedfam-IPEC 472 Scaled PolisherDown Pressure (PSI) 1 4 4
Platen Speed Reynolds Number Relative pad-wafer velocity of 0.5 m/sec (30 rpm)
Relative pad-wafer velocity of 0.5 m/sec (55 rpm)
Platen Diameter / Wafer Diameter
Dplaten / Dwafer 51 cm / 20 cm 31 cm / 12 cm
Slurry Flow Rate (cc/min)
Platen Surface Area 175 65
95
2.1.2 Table Top Polishing Platform
The Struers tabletop polisher was manufactured with several features that were used
in the polishing experiments for this research. The polisher was pre-calibrated for
variable platen rotation rates by the manufacturer, however the as-received settings were
manually verified using a tachometer. The other primary feature of the polisher that was
used in several experiments from this research was the inline water-channeling feature,
which allowed externally heated or cooled water to be channeled through the polisher and
be radially dispersed below the platen surface. This enabled heating or cooling of the
platen for temperature specific polishing studies. Further details of this system are
discussed in Chapter 2.1.9.
2.1.3 Wafer Carrier and Polishing Head Mechanism
As seen in Fig. 2.1, a modified industrial drill press with the ability to rotate and
apply an appropriate amount of down pressure was used as the wafer carrier. A weight
carriage mounted on a traverse provided variable pressure onto a gimbaled wafer carrier.
The chuck of the drill press was used to position and hold the brass post of the wafer
carrier, seen in Fig. 2.3, such that the carrier would be positioned at a height upon pad
contact which would ensure the traverse being parallel with ground (this would guarantee
an accurate applied wafer pressure based on traverse calibrations).
96
The rigid-backed wafer carrier shown in Fig. 2.3 was comprised of a flat 4.5-inch
aluminum disc with a poromeric backing film template glued onto the disc. The carrier
template contained a retaining ring which excluded 0.25 inches of the total aluminum
disc diameter, thus allowing 4-inch diameter wafers to fit within the template. The wafer
was held onto the backing of the carrier with water adhesion. The retaining ring depth
was less than the thickness of the wafer such that the wafer could make sole contact with
the pad surface during the polishing.
A DC controller integrated into the drill press controlled the wafer sliding velocity.
By changing the input voltage of the controller, sliding velocities could be varied to
specific settings. Figure 2.4 shows the calibration curve that was used to adjust wafer
sliding velocities with dial settings on the DC controller. Figure 2.4 shows a linear trend
of velocities with dial settings.
89.27int)(84.1 −⋅= posetdialRPM (2.2)
The linear fit for this trend is shown in Eqn. (2.2). Note the negative y-intercept of
Eqn. (2.2), which indicates that below a dial setting of approximately 20, no rotation
would occur.
97
Figure 2.3: Image of wafer carrier with poromeric carrier template
Figure 2.4: DC controller calibration plot for wafer sliding velocity
Wafer
Brass Post
Retaining Ring
Wafer
Brass Post
Retaining Ring
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70 80 90 100
Dial Set Point
Waf
er S
lidin
g Ve
loci
ty (R
PM)
98
2.1.4 Force Transducer Calibration
Figure 2.5 shows the apparatus constructed for force transducer calibrations. An
accurate force transducer calibration was critical for a reliable traverse and applied wafer
pressure calibration. As seen in Fig. 2.5, a metal rod was inserted into a slot on the
apparatus and a metal plate above that. A set of weights would then be placed on top of
this plate such that the position of the weights would be directly centered over the
transducer.
Calibration of the transducer began by recording an initial voltage with no weights. In
theory, the observed voltage of the transducer with no weights should read zero, however
any deviations from this were corrected by re-zeroing the reading within the computer
program used for this calibration. The transducer used for these calibrations was accurate
to within ± 0.5 volts.
The calibration process would continue with the incremental addition of more weight
(0 to 70 lbs) on the calibration apparatus. Corresponding voltage readings for each weight
set can be seen in Fig. 2.6. Equation (2.3) represents the linear calibration trend seen in
Fig. 2.6.
37.2)(66.3 −⋅= weightVoltage (2.3)
99
Figure 2.5: Force transducer calibration apparatus
Figure 2.6: Force transducer calibration plot
Force Transducer
Weights
Rod
Supports
Force Transducer
Weights
Rod
Supports
0
50
100
150
200
250
300
0 10 20 30 40 50 60 70 80
Weight (lbs)
Volta
ge (m
V)
100
2.1.5 Traverse Calibration
To calibrate the traverse shown in Fig. 2.7, a brass rod was placed into the chuck of
the drill press and positioned on top of a force transducer. The height and position of the
brass rod was such that the traverse would lie parallel with the ground (a level was used
to verify this) upon contact with the transducer. At this point, the weighted carriage was
shifted along the traverse via a stepper motor, which was mounted to the end of the
traverse. Based on the position of the weight carriage on the traverse, various
measurements would be recorded from the force transducer.
The initial traverse position, or zero position, was set at the point that would be
closest to the pivot point of the drill press without tipping the traverse and weights
backwards. When a weight of 65 lbs was mounted on the carriage, the pressure for a 4-
inch wafer at the zero point was 1.8 PSI. This indicates the lowest applied wafer pressure
of the tool. To determine the exact applied wafer pressure as a function of traverse
position, the mean pounds encountered by the force transducer was plotted against the
number of steps away from the zero point (see Fig. 2.8). This calibration also showed a
linear relationship and can be represented in the form of Eqn. (2.4).
57.22)(25.0 +⋅= stepsWeight (2.4)
Conversions to applied wafer pressure simply required one to divide the given weight
values by the wafer area.
101
Figure 2.7: Drill press with a mounted weight traverse
Figure 2.8: Traverse calibration plot for applied wafer pressure
0
20
40
60
80
100
0 500 1000 1500 2000 2500 3000
Steps
Wei
ght (
lbs)
102
2.1.6 Friction Table
Figure 2.9 is a side view schematic of the polisher setup used for friction table
calibrations. As mentioned earlier, a strain gauge positioned between two steel plates
measured the shear force at the pad-wafer interface during polishing. The strain gauge
used in this research could withstand up to 75 lbs of shear force. Figure 2.9 shows a
pulley system that joined one end of the movable top plate with a set of weights that hung
over the edge of the isolation table. This setup allowed for variable lateral forces to be
applied to the strain gauge of the friction table by changing of amount of weight hanging
over the edge of the isolation table.
Calibration of the friction table began by recording the voltage of the strain gauge
with no weights. This would ensure that a zero voltage would be read under zero weight
conditions. The calibration process would continue with the incremental addition of
weights on the pulley and the recording of corresponding voltage readings for each
weight set. A calibration curve for the strain gauge voltage can be seen in Fig. 2.10.
Equation (2.5) represents the linear calibration trend seen in Fig. 2.10. Based on this
calibration, real-time voltage readings taken during polishing by the strain gauge could
directly be corresponded to a shear force and thus COF (see Eqn. (2.1)).
03.0)(48.0 −⋅= weightVoltage (2.5)
It should be noted that the strain gauge was also calibrated such that the pulley was
positioned normal to the direction of sliding. This calibration was performed to ensure
that frictional readings were only being generated in the direction of sliding and were not
103
lost to an alternate axis. Results showed that less than one percent of the total force was
experienced in the normal direction, thus ensuring that nearly 99 percent of the total
frictional signal was accurately detected in the shear direction (Charns, 2003).
On a final note, stain gauge (i.e., frictional) readings taken during polishing were
subject to many sources of signal error resulting from tool vibration. High applied wafer
pressures, sliding velocities or dilute slurry concentrations were common sources of
unintentional tool vibration. In order to eliminate these unnecessary frictional events,
frictional baselines were taken prior to polishing experiments. Baselines were taken such
that every component of the polisher would be in motion with the exception of the wafer
on the pad. These baselines would then later be used to subtract out any frictional noise
not associated with the pad and wafer contact mechanism.
Figure 2.9: Side view schematic of friction table calibration set-up
Sliding Friction Table
Strain Gauge
Isolation Table
Tabletop Polisher
Weight
Sliding Friction Table
Strain Gauge
Isolation Table
Tabletop Polisher
Weight
104
Figure 2.10: Strain gauge calibration plot
2.1.7 Pad Conditioning System
The pad conditioning system consisted of a 2-inch diamond-conditioning disc, which
was spring-loaded onto the pad. The diamond-conditioning disc was held in place with a
chemically and mechanically resistive polyphenylene-based housing (this design was
similar to the wafer-carrier mount described before). The spring length and spring
constant were selected such that the applied down pressure was approximately 0.5 PSI on
the pad. The pressure calibration of the spring was performed using a Tekscan® pressure
mapping system and will be discussed in detail in Chapter 3.2.2. Figure 2.11 shows the
0
0.5
1
1.5
2
2.5
3
3.5
0 10 20 30 40 50 60 70
Weight (lbs)
Volta
ge (V
)
105
pad conditioning apparatus during polishing. As seen in the figure, the conditioner was
designed to perform in-situ or ex-situ. Alternate conditioning schemes were possible by
removing or attaching the conditioner apparatus on pre-positioned brackets installed on
each side of the polisher.
96.4)(11.69 −⋅= voltsRPM (2.6)
23.10)(21.70min/ −⋅= voltsosc (2.7)
Two stepper motors allowed the conditioning disc to rotate and sweep independently
across the pad. The calibration of the stepper motor involved a trail and error procedure
of estimating rotation and oscillation rates (per minute) with various input voltages.
Figure 2.12 (a) and (b) show the calibration plots for the rotation and oscillation of the
conditioner motors respectively. The observed linear trends could also be described by
Eqns. (2.6) (rotation calibration) and (2.7) (oscillation calibration).
106
Figure 2.11: Pad conditioning apparatus during in-situ polishing
Figure 2.12: Calibration plots for diamond pad conditioner (a) rotation motor and (b) oscillation motor
(a) (b)
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1 1.2
Voltage (V)
Rota
tion
Velo
city
(RPM
)
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1 1.2
Voltage (V)
Osc
illat
ions
per
Min
ute
(a) (b)
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1 1.2
Voltage (V)
Rota
tion
Velo
city
(RPM
)
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1 1.2
Voltage (V)
Osc
illat
ions
per
Min
ute
107
2.1.8 Slurry Distribution System
As seen in Fig. 2.11, slurry was distributed with Tygon® tubing onto the center of the
pad. In order to maintain a consistent slurry distribution position during polishing, the
tubing was run through a semi-rigid aluminum casing, which was specifically crafted to
resist movement. The drive for slurry distribution was provided by a Masterflex®
peristaltic pump. The pump would transport slurry from a pre-formulated slurry source
(i.e., beaker) to the pad.
As-received, the pump was calibrated through simple flow rate tests. If a specific
flow rate setting on the pump resulted in more or less than what was expected, then
positive and negative adjustments to the pump rotation rate would be made to correct the
issue. These adjustments would then be re-verified to ensure accurate pump rates. Figure
2.13 shows the calibration plot for the pump used in this research.
108
Figure 2.13: Peristaltic pump flow rate calibration plot
0
100
200
300
400
500
600
0 50 100 150
Flow Rate (cc/min)
Pum
p R
otat
ion
(RPM
)
109
2.1.9 Platen Temperature Control System
To control the platen temperature for polishing, the platen-cooling feature of the
Struers polisher was used to introduce high flow rates of water, at varying reservoir
temperatures, through a radial channel located beneath the platen. Various experiments
performed in this research required reservoir temperatures that were controlled such that,
during CMP, the polishing pad could reach a desired steady state temperature. This meant
maintaining relatively consistent reservoir temperatures. Experiments conducted in
Chapters 5.2 and 5.3 involved water reservoirs whose temperatures were controlled with
hot plates. The temperature of water reservoirs used in the experiments of Chapter 4
involved the application of a semi-circulating heat-exchanger bath (this proved slightly
more thermally stable). Figure 2.14 shows a box diagram of the temperature controlled
water bath system used in the latter experiments. The semi-closed-loop system seen in
Fig. 2.14 allowed heated or cooled water to pass beneath the platen radially outwards,
thus combining with the slurry waste stream and leaving the polisher in a single pass. All
experiments using below room temperature platen conditions implemented ice baths.
For each respective experiment, the desired polishing temperatures were defined by
thermal readings taken on the pad surface by an Infra-Red (IR) camera. Details of this
temperature recording system will be discussed in further detail in Chapter 2.3.2. Based
on the deviation between the desired pad temperature (set-point temperature) and the
observed IR reading, temperature adjustments were made by increasing or decreasing the
110
flow rate of reservoir fluid to the polisher, or by adjusting the reservoir temperature. The
latter was less favorable due to long heating and cooling times.
Figure 2.14: Box diagram of temperature controlled water bath system from experiments conducted in Chapter 4
Polisher Waste
Water Bath at Temperature, T
Pump
Polisher Waste
Water Bath at Temperature, T
PumpPump
111
2.1.10 Computer Automation
All of the described calibrations for each individual component of the polisher were
incorporated into a computer interface created in National Instrument’s LabVIEW
software. This polishing interface program was originally developed at Tufts University.
With the exception of wafer speed control, all other components of the polisher could be
automated by this computer interface. The LabVIEW program developed for this polisher
allowed for data acquisition (i.e., shear force) as well as data analysis.
The general setup within LabVIEW entailed the real-time acquisition of voltage
signals from the polishing tool components via a National Instruments connector block.
Each voltage-based calibration was programmed, by code, into the LabVIEW interface.
In turn, the LabVIEW interface enabled users of the polisher to input and read polishing
parameters such as sliding velocity and slurry flow rate in their actual metrics and not in
terms of voltage.
2.2 Sandia National Laboratory SpeedFam-IPEC Avanti 472 Platform
Several studies performed in the course of this research were done on the SpeedFam-
IPEC Avanti 472 rotary polisher. The polisher was located at Sandia National
Laboratory’s (SNL) Microelectronics Development Laboratory (MDL) in Albuquerque,
New Mexico. Figure 2.15 provides a frontal view of the industrial scale tool.
112
Since the introduction of the commercial CMP tools, the SpeedFam-IPEC rotary tool
has long been regarded as the most stable and reliable, especially with ILD applications.
It was for this reason that the polisher used at the IPL was scaled based on this industrial
tool. The polishing tool was a single spindle, single wafer processing system. The wafers
polished on the polishing tool were 6-inches in diameter and were held to the back of the
wafer carrier system using an in-line vacuum system. The rigid carrier head was also
designed with a poromeric backing for additional adhesion of the wafer.
The polishing tool was also designed with a secondary platen intended for buffing
following the primary removal step. This step in polishing varied significantly with the
primary polishing step in terms of processing parameters (high velocity and low
pressures) and consumables (soft felt-like polishing pads).
Controls for changing polishing parameters such as applied wafer pressure, sliding
velocity and slurry flow rate were done through the polisher’s internal computer
interface. Weekly tool calibrations were performed by SNL technicians to ensure reliable
tool kinematics and polishing performance.
113
Figure 2.15: Front view of SpeedFam-IPEC 472 rotary CMP tool
114
2.2.1 Pad Conditioning System
The pad conditioning system on the SpeedFam-IPEC 472 was an Advanced Pad
Profiler (APP-1000) diamond conditioning system. Diamond conditioning discs were
101-mm in diameter and varied in grit size and design. The conditioner track was
designed on the tool such that conditioning could be done in-situ or ex-situ. Conditioning
pressure, rotation rate and sweep rate were held constant during processing, however
could be changed using the polishers internal computer interface.
2.2.2 Luxtron Motor Current Endpoint Detection System
Luxtron’s Optima 9300 CMP endpoint system was used for detecting motor current
signals from the polishing tool. The Optima 9300 was supplied with four current sensors,
of which only two were used. One sensor was attached to the carrier-head and the other
to the platen. Both sensors were capable of acquiring current signals at a frequency of 10
Hz, and could accommodate direct or alternating currents of up to 25 A. The sensors
were also capable of detecting current changes of less than 2 mA. As motor current
signals were detected during polish, the real-time controller (RTC) of the Optima 9300
allowed the system to record and recognize endpoint conditions as they occurred on the
polishing tool. Once the system detected an endpoint, a relayed signal was sent to the
polishing tool via a serial I/O interface (Luxtron Corporation, 1999).
115
Figure 2.16 is a block diagram of the set-up. Further details about the Luxtron system
will be discussed in Chapter 6.
Figure 2.16: Block diagram of an integrated Luxtron motor current EPD system
IPEC-AVANTI 472
Luxtron Optima 9300
Console
Endpoint Signal Relay
Real Time Controller
From Platen
From Carrier-Head
IPEC-AVANTI 472
Luxtron Optima 9300
Console
Endpoint Signal Relay
Real Time Controller
From Platen
From Carrier-Head
116
2.2.3 Platen Temperature Control System
To control the primary platen temperature on the SpeedFam-IPEC 472 tool, an
internal heat exchanging system was used for platen heating and an external chiller was
used for platen cooling. Temperature settings were adjusted using the computer interface
of the polishing tool. Unlike the scaled down version of the tool, the platen temperature
control system on the polishing tool was completely re-circulating, thereby creating fewer
thermal fluctuations. This closed-loop system allowed heated or cooled fluid to pass
beneath the platen radially outwards, be captured without slurry contamination, pass
through the exchanger system and return to the platen.
The pad surface temperature was monitored using an IR camera prior to and during
each polish. Details of this temperature recording system will be discussed in further
detail in Chapter 2.3.2. As a final note, it should be mentioned that the thermal stability
on the polishing tool was superior to that of the scaled down version of the tool at the
IPL.
2.3 Metrology Equipment
To evaluate pad material properties and the results from thousands of polishing
experiments several metrology instruments were utilized. Since certain studies were
conducted at different locations (IPL and SNL), the same analysis was regularly done
117
using different make and model metrology tools. The underlying operation principles of
these tools are similar.
2.3.1 Thermo-analytical Instruments
CMP is very sensitive to temperature, both chemically and mechanically. As
mentioned before, the frictional interactions that occur at the pad-wafer interface alone
can create fluctuations of heat that can promote or hinder the removal process during
CMP. Understanding the material property changes as a result of this heat could provide
insight towards various phenomena that occur during polishing. Based on this premise,
studies were performed to determine the dynamic physical properties of polishing pads.
The term dynamic should be highlighted because it declares a differentiation between
the isothermal and non-isothermal conditions used for determining these properties.
Material properties such as Young’s modulus, or elongation, are reported based on tests
done at an isotherm (commonly ambient, 24°C). Dynamic material properties such as
storage modulus, or loss modulus, take into consideration the effects of changing
temperature as part of the reported result.
Since CMP is a thermally dependent process, characterizing the material properties as
a function of temperature is an appropriate means of describing the possible effects
during polishing. Performing dynamic analysis of polishing pads yields the mechanical
properties of the pad material while taking into account the energy dissipation (as heat)
118
during deformation. Performing traditional material tensile analysis occurs only at
specific isotherms and would not properly describe the events that occur during CMP.
2.3.1.1 Dynamic Mechanical Analyzer
Dynamic pad properties such as storage modulus and loss modulus were found using
TA instrument’s dynamic mechanical analyzer (DMA) 2980 (see Fig. 2.17). The DMA
measures the viscoelastic response of a pad sample as a function of a constant sinusoidal
stress and changing temperature. To achieve these testing conditions, polishing pad
samples were cut as rectangles (approximately 17.2 mm × 13.3 mm × 1.3 mm) and
placed into a single cantilever system within an isolated chamber. Within the chamber,
the long ends of the pad sample were clamped with a torque wrench (approximately 6
lbs), where one end was fixed in position and the other was free to oscillate sinusoidally.
During testing, the chamber would be closed off and an internal heating/cooling system
would change the temperature at a designated rate.
The experimental conditions used for CMP pad testing included a thermal ramping
rate of 5°C/min from -110°C to 200°C. The oscillation rate of the pad was held at
approximately 70 µm/min. Resulting mechanical responses were detected by the tool and
reported as a function of temperature.
119
Figure 2.17: TA Instruments Dynamic Mechanical Analyzer 2980 at the IPL
The following are definitions of the analytical results obtained from the DMA:
Glass Transition Temperature (Tg) – The temperature at which a material changes
from glass-like properties to rubber. When analyzing this parameter with the DMA, Tg
can either be detected by a distinct onset of the storage modulus vs. temperature curve, or
a distinct peak on the loss modulus vs. temperature curve (see Fig. 2.18). The Tg range for
most polyurethane based polishing pads is approximately -20°C to -5°C.
Storage Modulus – A term used to quantify the dynamic elastic energy stored in a
specimen due to an applied strain and is usually described in units of MPa. In general, it
is considered a measure of a material’s bulk softening with changing temperature and can
also be an indicator of a specimen’s glass transition temperature (Tg). Figure 2.18 shows
the indicating point for the storage modulus Tg of a polishing pad and the slope range that
is often considered for determining the extent of pad softening. Storage modulus has a
120
flexural (E’) and shear component (G’), which are dependent on the direction of phase
angle during testing. Equations (2.8) and (2.9) define these parameters
')1(2' GE ⋅Σ+= (2.8)
δσ cos'o
o
eG = (2.9)
In the above equations, Σ is a poison ratio constant for isotropic materials, σo is stress,
eo is strain and δ is the phase lag angle obtained from specific testing conditions. The
phase angle of the pad samples in DMA are such that the flexural component of storage
modulus is obtained.
Storage modulus, although different from Young’s modulus in principle, is often used
to define a materials mechanical strength. As it has been described above, the two
analytical parameters have distinctly different physical meanings, however in the CMP
research arena, both parameters are often used to define polishing pads. Since these
parameters are often interchanged and compared, it is important to realize their
relationship with one another.
Storage modulus can be related to Young’s modulus in the following manner. As seen
in Eqn. (2.10), Young’s modulus is defined as a measure of longitudinal strain (σ), or the
ratio of normal stress (ε) to the corresponding strain for tensile or compressive stresses
less than the proportional limit of the material.
εσ
=E (2.10)
121
Figure 2.18: Typical DMA results for a polyurethane based polishing pad
If one considers the fact that the DMA provides the flexural storage and loss modulus
components for a material, then one can calculate a complex modulus (E*) defined as
"'* iEEE += , (2.11)
where E” is flexural loss modulus. As the flexural storage modulus increases such
that the magnitude of (E”/E’) approaches zero, only then can one consider the complex
modulus equal to the Young’s modulus (i.e., E* = E). In practical terms, this dynamic
limit is indicative of a material being purely elastic.
Loss Modulus – A term used to quantify the dissipation of energy of a specimen as a
function of temperature and is usually described in units of MPa. In a general sense, this
-51.91°C
-38.90°C
-34.03°C
0.05
0.10
0.15
0.20
Tan
Del
ta
0
50
100
150
200
Loss
Mod
ulus
(M
Pa)
0
500
1000
1500
2000
2500S
tora
ge M
odul
us (
MP
a)
-150 -100 -50 0 50 100 150 200
Temperature (°C) Universal V3.8B TA Instruments
E’
E”
Tan δ
Onset point, Tg
Loss modulus peak, Tg
Storage modulus decrease (20°C – 45°C)
Tan δ peak, Tg
-51.91°C
-38.90°C
-34.03°C
0.05
0.10
0.15
0.20
Tan
Del
ta
0
50
100
150
200
Loss
Mod
ulus
(M
Pa)
0
500
1000
1500
2000
2500S
tora
ge M
odul
us (
MP
a)
-150 -100 -50 0 50 100 150 200
Temperature (°C) Universal V3.8B TA Instruments
E’
E”
Tan δ
Onset point, Tg
Loss modulus peak, Tg
Storage modulus decrease (20°C – 45°C)
Tan δ peak, Tg
122
parameter is an indicator of a material’s glass transition point and is identified by a signal
peak over the tested temperature range. Loss modulus has a flexural (E’’) and shear
component (G’’), which is dependent of the direction of phase angle during testing.
Equations (2.12) and (2.13) define these parameters.
")1(2" GE ⋅Σ+= (2.12)
δσ
sin"o
o
eG = (2.13)
Tan δ – A parameter that is calculated as the ratio of flexural loss modulus to storage
modulus (see Eqn. (2.14)). This term is used to indicate the toughness of a specimen
(based on area calculations underneath the resulting signals) and can only be compared
relative to comparable signal results. This parameter can also be used as an indicator of
the glass transition for a specimen (see Fig. 2.18).
'"tan
EE
=δ (2.14)
2.3.1.2 Thermo-Mechanical Analyzer
Dynamic pad properties such as coefficient of thermal expansion (CTE), Tg and the
extent of pad compressibility (softening) were found using TA Instrument’s thermo-
mechanical analyzer (TMA) 2940 (see Fig. 2.19). The TMA measures the thermal
expansion and contraction responses of a pad sample as a function of height displacement
under a constant applied force and changing temperature (i.e., the TMA measures height
123
displacements). To achieve these testing conditions, square centimeter polishing pad
samples were cut and placed on a quartz platform within an isolated chamber. Within the
chamber, a quartz expansion probe (diameter of 2.8-mm) would press against the sample
surface with a constant force. During testing the chamber would be closed off and an
internal heating/cooling system would change the temperature at a designated rate.
At the initial point of testing, the probe would be positioned on top of a pad sample
and calibrated such that the initial height of the probe would be considered zero. As the
TMA chamber temperature would rise, the pad sample would undergo physical
expansion and contraction. These effects would consequently alter the height of the
probe, thus generating results which would indicate a pads compressive reaction to
changes in temperature.
The most critical result that was generated from TMA testing was the calculation of
the extent of compression, or softening, over the range of temperatures commonly
experienced in CMP (approximately 20°C – 45°C). Figure 2.21 shows typical TMA
results for a conventional polyurethane based polishing pad. The figure shows the region
in which this softening parameter is calculated. Ideally, one would desire a polishing pad
whose dimensional change (y-axis) would be unaltered over typical polishing
temperatures (i.e., flat curve segment). This would ensure consistent pad mechanical
properties during polishing, regardless of temperature. However, as it can be seen from
Fig. 2.21, the polishing pad tested does not exhibit this type of ideal behavior, which
could indicate potential pad deformation during polishing thus compromising
performance. Figure 2.21 also shows the acquisition points for CTE and Tg.
124
The experimental conditions used for CMP pad testing included a thermal ramping
rate of 6°C/min from -110°C to 180°C. The constant load applied on the pad sample
throughout testing was 0.1 N.
Figure 2.19: TA Instruments Thermo-Mechanical Analyzer 2940 at the IPL
125
Figure 2.20: Schematic of TMA internals
Platform with Probe
Removable Isolation Chamber
Platform with Probe
Removable Isolation Chamber
126
Figure 2.21: Typical DMA results for a polyurethane based polishing pad
2.3.2 Infra-Red Temperature Measurements
IR thermography was needed for temperature specific polishing studies. Ideally one
would desire knowing the temperature events directly underneath the wafer during
polishing, however the design of such sensors would prove difficult when considering the
dynamic intricacies during CMP. IR thermography was the next best solution for the task
of thermal detection. IR data was obtained using an Agema® Thermovision 550 IR
camera. The camera was calibrated as-received from the manufacturer and was verified at
IPL by measuring surfaces of known temperatures.
-2.29°C(I)
-51.47°C
4.11°C
14.13°C
107.28°CAlpha=114.9µm/m°C
-60
-40
-20
0
20
40
60
80
Dim
ensi
on C
hang
e (µ
m)
-150 -100 -50 0 50 100 150 200
Temperature (°C) Universal V3.8B TA Instr
Onset point, Tg
Coefficient of Thermal Expansion, CTE
Extent of Pad Softening (20°C – 45°C)
-2.29°C(I)
-51.47°C
4.11°C
14.13°C
107.28°CAlpha=114.9µm/m°C
-60
-40
-20
0
20
40
60
80
Dim
ensi
on C
hang
e (µ
m)
-150 -100 -50 0 50 100 150 200
Temperature (°C) Universal V3.8B TA Instr
Onset point, Tg
Coefficient of Thermal Expansion, CTE
Extent of Pad Softening (20°C – 45°C)
127
As seen in Fig. 2.22, the camera was mounted on an adjustable arm stand and
positioned such that the camera would capture nearly all of the wafer-head
circumference. The camera was connected to a local computer, which provided an
interface for camera control and recording. Once in position, recording would begin just
before the start of a polishing experiment. The camera recorded thermal images at
frequency of 5 Hz at ten points around the leading and trailing edges of the wafer (i.e.,
five points along each side of the wafer, see Fig. 2.23). Since direct thermal readings
could not be acquired in the pad-wafer interface, the above ten points along the periphery
of the wafer allowed for a suitable estimation of the mean process temperature
experienced during polishing. Based on this postulation, the mean process temperature
was calculated as the average value of the ten points taken over the entire duration of the
polish.
The IR camera was also used to monitor pad temperatures prior to polishing. Since
certain studies in this research required polishes to occur at specific thermal set points, IR
was used to monitor this temperature. Based on the IR readings, pad temperatures could
be adjusted such that the desired set point temperature for a polish could be reached (see
Chapters 2.2.3 and 2.1.9).
The only limiting aspect about IR was the fact that it could not record through
transparent or non-transparent materials. IR emission from any materials is only a surface
phenomena, thus limiting the extent to which the device could be used for determining
the true polishing temperature.
128
Figure 2.22: IR camera positioned during polishing
Figure 2.23: IR image of temperature controlled polishing. Spots 1 through 10 indicate the points of temperature detection along the leading edge (SP01 – SP05) and trailing edge (SP06 – SP10) of the wafer
22.3°C
31.6°C
24
26
28
30SP01
SP02
SP03
SP04
SP05
SP06
SP07
SP08
SP09
SP10
129
2.3.3 Film Thickness Measurements
Film thickness measurements were performed following all ILD polishes in order to
determine the removal rates and uniformity associated with a certain polishing process.
This analysis was done on an ellipsometer. The basic principle of an ellipsometer is to
measure the thickness of light-transparent material films by measuring the polarization
state of a light beam following its reflection on the material. This light source can be
varied in wavelength and is usually projected on the film sample at an oblique incidence
(Edwards, 2004). As film thickness on a wafer changes, so does the polarization
sensitivity of the reflected light. This change in polarization is then converted into a
specific film thickness that can measured on order of Angstroms.
Copper polishes performed in experiments from Chapter 5.2 were analyzed
differently. As it will be discussed in Chapter 5.2, the copper substrates used in those
experiments were copper discs. As a result of this, film thickness measurements were not
possible to determine removal rates. A substitute method for determining copper
polishing results was weight measurements. An OHAUS Analytical Plus® scale was
used to determine the amount of material removal to within a thousandths of a gram.
Tungsten polishes performed in experiments from Chapter 5.5.2 were analyzed using
a four-point probe at SNL. Four point probes determine material thickness on the
principle of electrical conduction through the metal sample. In the most basic sense, the
metal thickness varies inversely with the rate of conduction.
130
CHAPTER 3 – APPLIED WAFER PRESSURE EFFECTS DURING CMP
3.1 Motivation
As described in Chapter 1, the process parameters of pressure and velocity affect the
rate of material removal in a proportional manner. For an effective CMP process, it is
essential that the pressure applied on the wafer be distributed uniformly along the entire
area. This becomes difficult when one considers the dynamic intricacies of CMP as well
as possible structural issues with the wafer such as thermally induced bowing and feature
patterning. Advances in wafer carrier technology have alleviated some of these issues,
but have yet been able to correct pressure distribution issues in the case of significantly
warped wafers or wafers with diverse pattern density structures. Understanding the
fundamental impact of pressure in such cases could lead towards solutions for more ideal
CMP processing, specifically in the form of novel carrier designs or more stringent
polishing conditions. In the course of this research, the effects of wafer geometry (i.e.,
warping or bowing) and wafer pattern density on pressure were investigated.
131
3.2 Impact of Wafer Geometry and Thermal History on Pressure and von Mises Stress Non-uniformity During STI CMP
3.2.1 Background
One area of CMP that can potentially impact the mechanical attributes of the process
is the variation in wafer geometry as measured by the overall shape (i.e., extent and
direction of bow), and the nominal diameter of the wafer. The latter becomes more
critical as one considers normal variations in the inside diameter of the retaining ring and
the size of the wafer-ring gap resulting from such dimensional differences. Assuming the
above variations to follow Gaussian behavior, the probability of encountering wafer-ring
gap sizes as low as nominally zero mm or as high as 2 mm is calculated to be
approximately 0.004. This is significant since in high volume IC manufacturing facilities,
the number of CMP polishes can exceed 250,000 per month. Moreover, as wafers
progress through the manufacturing line, they undergo a series of high temperature
processes. Given the reported effects of heat treatment on the mechanical properties of
silicon wafers, (Senkader et al., 2001; Fukuda, 1995) it would be of interest to establish
potential correlations between the thermal history of wafers and within-wafer material
removal uniformity during CMP.
As 300-mm wafers are becoming mainstream, variations in wafer shape, wafer-ring
gap size and bulk properties (resulting from variations in the thermal history of each
wafer) are becoming more pronounced thus further necessitating a fundamental
132
investigation of their impact on polish performance. The importance of such a study is
justified given the direct relationship between removal rate and pressure as described by
Preston’s equation (see Eq. 1.7).
According to Preston’s equation, at any given region of the wafer, local removal rate
is directly proportional to local pressure. Moreover, since pressure and stress are related
to one another, variations in the overall stress experienced by the wafer are expected, to
some extent, affect the polishing outcome (Preston, 1927).
Several studies have focused on the extent of within wafer removal rate non-
uniformity resulting from wafer curvature (Zhang et al., 1996; Tseng et al., 1999; Chen et
al., 2002; Shaw et al., 2001; Sorooshian et al., 2003). Tseng et al., developed a
theoretical model that simulates pressure distribution occurring from wafer curvature
during CMP. The study demonstrated reasonable agreement between simulated pressure
data and oxide removal rate results from experimentation. Deviations between the
proposed model and the removal rate data are postulated to result from the stress induced
by slurry flow, local variations in wafer shape and pad surface properties (Tseng et al.,
1999).
Additionally, Chen et al. and Shaw et al. presented results of analytical studies
involving the kinematics and pressure distributions developed at the pad-wafer interface
during CMP. Overall, the results are in good agreement with their’ purposed numerical
simulations and clearly demonstrate that wafer curvature and non-uniformities in pressure
distribution affect the slurry film thickness in the pad-wafer region, the lubricity of the
system and the overall efficiency of the process (Chen et al., 2002; Shaw et al., 2001).
133
Until now, there have been no published data relating the effect of minor variations in
wafer diameter on within wafer removal rate non-uniformity. In general, no two wafers
or retaining rings have identical geometries, or undergo identical thermal cycles. In spite
of the fact that such variations may fall within the manufacturers’ product specifications,
tighter manufacturing control may be required in order to minimize within wafer non-
uniformity issues during CMP. This study employs actual pressure measurements and
von Mises stress simulations over the entire surface of the wafer in order to examine the
effect of the wafer-ring gap size, the extent and direction of wafer bow and the effect of
thermal history on within wafer non-uniformity (WIWNU) (Fujita et al., 2001; Wang et
al., 1997).
3.2.2 Experimental Approach
The pressure measurement experiments performed for this study were done at the IPL
and incorporated the use of the scaled polisher described in Chapter 2.1.
Pressure measurements were obtained with an automated Tekscan® pressure
mapping sensor. This pressure measurement technique was employed based on the
success of a study done by Fujita and Doi, who successfully employed this system for
analyzing pressure distribution across a 200-mm wafer supported by a novel air float
carrier (Fujita et al., 2001). The pressure sensor consisted of two thin, flexible polyester
sheets on which electrically conductive electrodes were deposited in varying patterns (see
Fig. 3.1). The inside surface of one sheet was patterned in the form of rows while the
134
inner surface of the other employs a columnar pattern. The spacing between rows or
columns was approximately 0.5 mm. At each node (i.e. the point where a row intersected
a column), an electrical resistance was provided courtesy of a thin semi-conductive ink
coating, which acted as an intermediate layer between the electrical contacts. When the
two polyester sheets were placed on top of each other, a grid pattern was formed, creating
a sensing location at each node. By measuring the changes in current flow at each node,
the applied force distribution pattern could be measured.
Wafer pressure distribution data was taken on a Rohm and Haas IC-1000 flat pad.
Prior to data acquisition, the pad was conditioned for 30-minutes in ultra pure water with
a 100-grit diamond disc at a pressure of 0.5 PSI, rotational velocity of 30 RPM and disk
sweep frequency of 20 per minute. Pad conditioning was followed by a 5-minute pad
break-in with a dummy wafer. Pressure mapping was performed under static conditions
with the sensor placed directly between the pad and the 100-mm wafer. Figure 3.2 is an
example of the resulting pressure contour map from which various pressure profiles could
be extracted.
The following parameters were investigated:
• Applied wafer pressures of 2 and 6 PSI
• Wafer-ring gap sizes of zero, 0.4, 1.0 and 1.4 mm (see Fig. 3.3)
• Extent of wafer bow (defined as the difference in vertical distance between the
center and edge of the wafer) at values of zero (i.e. nominally flat) and 15 µm (see
Fig 3.3). Noted that all non-thermally treated wafers were simply bare silicon
135
• Direction of wafer bow in terms of its concave or convex shape (applies only to
wafers having a nominal bow of 15 µm)
• Extent of heat treatment of the wafer prior to CMP. The control samples were not
exposed to high temperature processing, whereas the thermally treated samples
had approximately 1500 Å of nitride deposited on top of the bare silicon and
underwent a 5-hour nitrogen anneal at 1000°C
Figure 3.1: (a) Diagram and (b) schematic of the Tekscan® pressure measurement sensor
pressure resistive sheet
X-wires
Y-wires
protective laminate film
(a) (b)
pressure resistive sheet
X-wires
Y-wires
protective laminate filmpressure resistive sheet
X-wires
Y-wires
protective laminate film
(a) (b)
136
Figure 3.2: Two-dimensional contour pressure image of a flat 100-mm diameter wafer at an applied wafer pressure of 6 PSI
Figure 3.3: (a) Top view schematic of wafer-ring gap and (b) side view schematic of concave and convex wafer geometries and extent of bow
Wafer
Carrier Ring
Wafer-ring gap
Convex wafer Extent of wafer bow
Concave waferExtent of wafer bow
Polishing pad
Polishing pad
(a) (b)
Wafer
Carrier Ring
Wafer-ring gap
Wafer
Carrier Ring
Wafer-ring gap
Convex wafer Extent of wafer bow
Concave waferExtent of wafer bow
Polishing pad
Polishing pad
Convex wafer Extent of wafer bow
Concave waferExtent of wafer bow
Polishing pad
Polishing pad
Convex wafer Extent of wafer bow
Concave waferExtent of wafer bow
Polishing pad
Polishing pad
(a) (b)
137
3.2.3 Results and Discussion
3.2.3.1 Stress Simulations
The von Mises stress was selected as the output parameter of the simulations for this
study. Proposed by Ludwig von Mises in 1913, von Mises stress (Eq. 3.1) describes a
single stress component (σo) containing a combination of normal stresses (σx,y,z) and shear
forces (τx,y,z) acting on a body in their respective directions.
( ) ( ) ( ) ( )[ ]21
222222 62
1xzyzxyxzzyyxo τττσσσσσσσ +++−+−+−= (3.1)
The basic concept of the above equation was the following: Stress is defined as the
internal resistance per unit area of a body to an external applied force. For a 3-
dimensional system, stress can be accounted for in three directions (i.e., x, y and z). When
the combination of these principle stresses exceeds the yield stress of uni-axial tension
for the body, then yielding of that body occurs.
Further details regarding the definition and utility of von Mises stress in CMP
applications may be found elsewhere (Wang et al., 1997; Dieter, 1986).
The simulations for this study were completed assuming a 2-dimensional, axis-
symmetric model (i.e., x and z) representing directions normal and tangential to wafer
surface. It should be noted that only the normal component of the von Mises stress
simulations can be related to pressure measurements taken in the experimental stage of
this study. However based on prior studies by Wang et al., relationships showing
similarities between the normal and tangential components of the von Mises stress
138
distributions and removal rate profiles were presented. Based on this prior relationship,
results from this study will show close similarities between the normal and tangential
components of the von Mises stress and the experimental pressure profiles taken from
this study. Analysis assumed that the wafer stack was comprised of five distinct layers as
shown in Fig. 3.4. The entire system was considered to be static and dry, with a specified
pressure applied to the top of the wafer stack. The polishing pads were assumed to be
continuous with isotropic physical properties. For each simulation, the von Mises stress
was calculated as a function of position for a specified applied wafer pressure and wafer
stack property (see Table 3.1). It should be noted that wafers with varying diameters, and
hence varying wafer-ring gap sizes, could be specified as input parameters to the
simulator. It should also be noted that simulations did not take into account the extent or
direction of wafer bow. As such, all simulations were performed assuming a perfectly flat
wafer.
139
Figure 3.4: Schematic representation of the wafer stack used in the simulation model
Table 3.1: Wafer stack material properties assumed in the simulation model
Carrier
Carrier Film
Wafer
Polishing Pad
Platen
Retaining Ring
Wafer-ring gap sizeCenter line
x
z
Carrier
Carrier Film
Wafer
Polishing Pad
Platen
Retaining Ring
Wafer-ring gap sizeCenter line
Carrier
Carrier Film
Wafer
Polishing Pad
Platen
Retaining Ring
Wafer-ring gap sizeCenter line
x
z
Material Elastic Modulus (MPa) Poisson Ratio Density (kg/m3)Carrier 194,000 0.330 7920Carrier Film 4.13 0.400 1140Wafer 130,000 0.279 2330Retaining Ring 194,000 0.330 7920Pad 250 0.400 800Platen 194,000 0.330 7920
140
3.2.3.2 Within wafer Pressure and Stress Non-uniformity for Nominally Flat and Thermally Untreated Wafers
Once a contour pressure map was generated for a given set of conditions, the pressure
profile across the line segment originating from the center of the wafer and terminating at
the wafer edge was obtained. The line segment was selected such that it ran parallel to the
100-mm wafer’s primary flat. The actual pressure profile was then divided into two
regions as follows: A ‘central zone’ extending from the center of the wafer to a radial
distance of 34-mm, and an ‘edge zone’ continuing from a radial position of 35-mm up to
the edge of the wafer.
Figure 3.5 is an example of von Mises stress and pressure profiles obtained for a
wafer-ring gap size of 1.4-mm and applied wafer pressure of 2 and 6 PSI respectively.
Focusing first on the ‘central zone’ of the wafer (as described above), average pressure
remains constant at 1.2 ± 0.1 PSI for an applied wafer pressure of 2 PSI and 4.6 ± 0.3 PSI
for an applied wafer pressure of 6 PSI. It is apparent that these results are in qualitative
agreement with the von Mises stress simulations. As for the edge region, both measured
and simulated metrics exhibit a sharp peak approximately 6 mm from the edge followed
by a sharp drop at the wafer’s edge.
This indicates that simulated von Mises stress profiles are able to qualitatively
describe pressure non-uniformities in the wafer-pad region and can be used, albeit with
caution, to predict stress, and hence pressure, non-uniformities for larger size wafers. It
141
must be noted that the shapes of the stress profiles of Fig. 3.5 are consistent with previous
reports (Fujita et al., 2001; Wang et al., 1997).
Figure 3.5: Measured pressure and simulated von Mises stress for a nominally flat, thermally untreated wafer at 6 PSI (gap size = 1.4 mm)
Figure 3.6 shows examples of von Mises stress profiles for 200- and 300-mm wafers
under an applied pressure of 4 PSI and a wafer-ring gap size of 0.4 mm. Both profiles
show a gradual stress increase along the ‘central zone’ of the wafer, followed by large
stress variations near the edge. The stress peak for 100-mm wafers (Figs. 3.5 and 3.6)
occurs roughly 6 mm from the edge (at 2 and 6 PSI applied pressure), while those
corresponding to 200- and 300-mm wafers occur roughly 9 and 21 mm from the wafer
edge (at a 4 PSI applied pressure), respectively.
0.0
2.0
4.0
6.0
8.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative Radial Position
Pres
sure
(PSI
)
0.0
2.0
4.0
6.0
8.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative Radial Pos ition
von
Mise
s stre
ss (P
SI)
0.0
2.0
4.0
6.0
8.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative Radial Position
Pres
sure
(PSI
)
0.0
2.0
4.0
6.0
8.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative Radial Pos ition
von
Mise
s stre
ss (P
SI)
142
Figure 3.6: von Mises stress simulations for 200- and 300-mm wafers at an applied wafer pressure of 4 PSI and wafer-ring gap size of 0.4 mm
As edge exclusion specifications for measuring within-wafer non-uniformities trend
towards values less than 3 mm, above simulations indicate that understanding the extent
of within wafer pressure and stress non-uniformities will be essential as 300-mm wafers
become mainstream.
It should be noted that there has been some reported concerns regarding the realness
of the pressure distribution results from the experimental portion of this study due to pad
wear resulting from conditioning. By performing a 30-minute condition of the pad prior
to testing, it has been estimated that the resulting wear track on the pad could generate up
to 30 µm of height variation (approximately 10 µm/min) from the center to the edge of
the pad (Borucki, 2005). As a result of this potential wear, pressure measurements on the
0.0
2.0
4.0
6.0
8.0
10.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative Radial Position
von
Mis
es S
tress
(PSI
)0.0
2.0
4.0
6.0
8.0
10.0
0.0 0.2 0.4 0.6 0.8 1.0Relative Radial Position
von
Mis
es S
tress
(PS
I)
200 mm 300 mm
0.0
2.0
4.0
6.0
8.0
10.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative Radial Position
von
Mis
es S
tress
(PSI
)0.0
2.0
4.0
6.0
8.0
10.0
0.0 0.2 0.4 0.6 0.8 1.0Relative Radial Position
von
Mis
es S
tress
(PS
I)
200 mm 300 mm
143
outside edge of the wafer will vary relative to the center. This would lead to misleading
pressure distribution results due to the pad curvature and not the wafer. In order to verify
that conditioning did not have a significant effect on the experimental pressure results, a
set of identical tests were performed using an as-received IC-1000 flat pad, which is
assumed to have little topographical variation. By showing the pressure distribution
results have similar profiles between the two pads, it could be ensured that the original
results were generated as a result of the wafer geometry and not an artifact of the pad.
Figure 3.7: Contour pressure distribution maps for nominally flat wafers using an as received Rohm and Haas IC-1000 flat pad and a conditioned pad (30 minutes). Note that the pad center is oriented on the top left corner of each image
Pad Center
2 PSI
6 PSI
Pad Center
As-received pad
6 PSI
Pad Center
Conditioned pad
Pad Center
2 PSI
Pad Center
2 PSI
6 PSI
Pad Center
As-received pad
6 PSI
Pad Center
Conditioned pad
Pad Center
2 PSI
144
Figure 3.7 shows a side by side comparison of pressure distribution for two identical
wafer sets on a conditioned and non-conditioned pad. Based on the hypothetical wear
track generated on the pad, one would expect to see a ridge of pressure along the bottom
right corner of the pressure maps. As seen from the results however, the pressure
distributions for the conditioned pad do not indicate this suspected rise. Moreover, the as-
received pad also does not show this result. The consistency of such results was shown
throughout the span of wafers and applied pressures tested. From this analysis, it can be
said that the experimental pressure distribution results from this study are a function of
the wafers and wafer-ring gaps and not the possible wear track from conditioning.
3.2.3.3 Wafer-ring Gap Size versus Within-wafer Pressure Non-uniformity for the ‘Central Zone’ and ‘Edge Zone’ of Bowed, Thermally Untreated Wafers
As stated previously, each measured pressure profile was divided into a ‘central zone’
and an ‘edge zone’. In order to simplify visualization and interpretation of the data, the
average and the standard deviation of all data points within each zone were computed.
Figures 3.8 through 3.11 summarize the effect of wafer-ring gap size on pressure non-
uniformity. For a given set of process conditions, each bar represents measured pressure
values ranging from one standard deviation below the mean to one standard deviation
above the mean.
145
Figures 3.8 and 3.9 represent pressure results along the ‘central zone’ of the wafer for
applied wafer pressures of 2 and 6 PSI, respectively. Regardless of the wafer-ring gap
size, the extent of wafer bow has a large impact on pressure variability. Nominally flat
wafers exhibit low variability, whereas concave and convex wafers exhibit 2.5 to 7 times
greater pressure variations. The trends are independent of applied wafer pressure.
First, at a nominal gap size of zero mm, average pressure is lowest for concave, and
highest for convex wafers. This is due to the negligible gap size, which prevents bowed
wafers from conforming in response to the applied load. Eliminating the wafer-ring gap
allows the wafer to maintain its shape and its associated pressure profile in spite of the
external load.
Second, at larger gap sizes (0.4 to 1.4 mm), average pressure remains constant
regardless of wafer shape at 1.27 ± 0.27 PSI and 4.76 ± 0.74 PSI for applied wafer
pressures of 2 and 6 PSI respectively. This is due to the fact that larger gaps make
provisions for convex and concave wafers to relax their shapes in response to an applied
load.
Figures 3.10 and 3.11 represent pressure results along the ‘edge zone’ of the wafer at
pressures of 2 and 6 PSI, respectively. Results indicate that the extent and direction of
wafer bow has no effect on average pressure and variability. However, wafer-ring gap
size appears to have a strong effect on average pressure and variability. At a nominal
wafer-ring gap size of 0 mm, the average pressure is roughly 25 percent less than the
average pressure at larger gap sizes (0.4 to 1.4 mm). Furthermore, the pressure variability
at the 0-mm gap is approximately 30 percent lower than those at larger gaps.
146
Figure 3.8: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 2 PSI)
Figure 3.9: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 6 PSI)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
147
Figure 3.10: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 2 PSI)
Figure 3.11: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally untreated 100-mm wafer (applied wafer pressure of 6 PSI)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
148
3.2.3.4 Wafer-ring Gap Size versus Within-wafer Pressure Non-uniformity for the ‘Central Zone’ and ‘Edge Zone’ of Bowed, Thermally Treated Wafers
Figures 3.12 through 3.15 summarize the effect of wafer-ring gap size on pressure
non-uniformity for thermally treated wafers. Figures 3.12 and 3.13 represent pressures
along the ‘central zone’ of the wafer for applied wafer pressures of 2 and 6 PSI,
respectively. Similar to thermally untreated wafers, regardless of the wafer-ring gap size,
the extent of wafer bow has a large impact on pressure variability. Nominally flat wafers
exhibit low variability, whereas concave and convex wafers exhibit 2.5 to 4.5 times larger
pressure variations. Again, trends are independent of applied wafer pressure.
Unlike thermally untreated wafers, heat treatment reduces or masks the effect of gap
size on average pressure in the ‘central zone’ of the wafer. Regardless of wafer-ring gap
size, average pressure in the ‘central zone’ remains at 1.32 ± 0.33 PSI and 4.28 ± 0.74
PSI for applied wafer pressures of 2 and 6 PSI respectively. Increases in the intrinsic
stress of the silicon wafer due to thermal annealing (Senkader et al., 2001; Fukuda, 1995)
are believed to reduce the effect of wafer-ring gap size on pressure variability.
Consistent with the above argument, at the ‘edge zone’ of the wafer, Figs. 3.14 and
3.15 indicate that wafer-ring gap size as well as extent and direction of wafer bow have
no effect on pressure and variability. Regardless of wafer-ring gap size, average pressure
in the ‘edge zone’ remains at 1.82 ± 1.15 PSI and 4.52 ± 2.20 PSI for applied wafer
pressures of 2 and 6 PSI respectively.
149
As seen in Figs. 3.10, 3.11, 3.14 and 3.15, a major effect of thermal treatment is the
increase in overall pressure variability at the ‘edge zone’ of the wafer for thermally
treated wafers. On the average, pressure variability is 17 percent higher for thermally
treated samples compared to the control samples.
Figure 3.16 is a qualitative illustration of how higher intrinsic wafer stresses may
result in an increase in the overall pressure variability at the ’edge zone’ of thermally
treated wafers. For purposes of illustration, the elastic modulus of a thermally treated
200-mm wafer has been increased from the original value of 130 to 260 GPa, while
maintaining values of the other parameters cited in Table 3.1. The choice of 260 GPa is
quite arbitrary since no published values of the elastic modulus for thermally treated
wafers have been found. In the case of Fig. 3.16, applied wafer pressure was set to 6 PSI
with a wafer-ring gap size of 0.4 mm. Results of the von Mises simulation are in
qualitative agreement with the observed experimental trends, thus indicating that
measured increases of pressure variability at the ‘edge zone’ as a result of heat treatment
may be explained by variations in the wafer elastic modulus and the interfacial stress in
this region.
150
Figure 3.12: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 2 PSI)
Figure 3.13: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘central zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 6 PSI)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mmAver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
151
Figure 3.14: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 2 PSI)
Figure 3.15: Effect of wafer-ring gap size and extent of wafer bow on pressure distribution along the ‘edge zone’ of a thermally treated 100-mm wafer (applied wafer pressure of 6 PSI)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm
0
1
2
3
4
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0.4 mm0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.0 mm0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 1.4 mm0
2
4
6
8
10
12
15(concave)
0 15(convex)
Extent and Direction of Wafer Bow (Micron)
Wafer-Ring Gap ~ 0 mm
Aver
age
Pres
sure
Plu
s &
Min
us 1
-Sig
ma
(PSI
)
152
Figure 3.16: Simulated von Mises stress for a nominally flat 300-mm wafer at 6 PSI (gap size = 0.4 mm)
0
2
4
6
8
10
0 20 40 60 80 100Radial Position (mm)
von
Mis
es S
tress
(PSI
)
Wafer Modulus = 130,000 MPa
Wafer Modulus = 260,000 MPa
0
2
4
6
8
10
0 20 40 60 80 100Radial Position (mm)
von
Mis
es S
tress
(PSI
)
Wafer Modulus = 130,000 MPa
Wafer Modulus = 260,000 MPa
Wafer Modulus = 130,000 MPa
Wafer Modulus = 260,000 MPa
153
3.2.4 Concluding Remarks
The above results demonstrate that variations in wafer geometry, as measured by the
overall shape (i.e., extent and direction of bow), nominal diameter and thermal treatment
of the wafers, can significantly affect the extent of pressure experienced by the wafer
during CMP. By applying Preston’s equation to a sampling of the experimental average
pressure and variability data presented above, it may be shown that removal rate can vary
significantly across the wafer surface depending on the extent and direction of wafer
bow, the wafer-ring gap size and the thermal history of the wafer (Preston, 1927).
Solving for removal rate using pressure data obtained from a stationary system can be
justified since pressure data presented in this work mimics those obtained using a
dynamic pressure mapping apparatus as demonstrated by Fujita and Doi (Fujita et al.,
2001).
To provide an example, assuming a Preston’s constant of 1.2 × 10-13 Pa-1 for ILD
CMP using IC-1000 pads, removal rate in the ‘edge zone’ can range from 400 to 800
Å/min for a concave, thermally untreated wafer having a wafer-ring gap size of 1.0 mm
(applied pressure of 2 PSI, and a wafer-pad velocity of 0.62 meters per second) (Olsen,
2002). Removal rate variations are expected to increase by approximately 20 percent for
thermally treated silicon wafers. Additionally, a two-fold increase in removal rate would
be expected at an applied pressure of 6 PSI with all other polishing parameters held
constant.
154
It has been shown that wafer-ring gap size, wafer shape, and thermal history cause
significant variations in pressure within a given wafer. This fact, couple with the
dependence of pressure on removal rate (i.e., in accordance with Preston’s equation),
implies that each wafer will experience a different local removal rate depending on the
pressure observed at a given location on the wafer. The generalized definition of
WIWNU is as follows (Sugimoto et al., 1995):
100×=average
RR
RRWIWNU σ
(3.2)
In the above equation, for a given number of film thickness measurements, σRR
represents the standard deviation of the removal rate and RRaverage represents the average
removal rate. Based on the results presented in this study, one can expect within wafer
non-uniformity values to range from 10 to 50 percent when considering the pressure non-
uniformities measured at 2 PSI applied pressure for the thermally untreated wafers
described above. Similarly, when applied pressure is increased to 6 PSI one would expect
within wafer removal rate non-uniformity for thermally treated wafer to be as high as 74
percent.
The above results demonstrate that variations in wafer geometry can significantly
affect the extent of WIWNU and ILD removal rate. In addition, these results draw
attention to the importance of adopting tighter manufacturing control limits in order to
minimize WIWNU issues during CMP.
155
3.3 Estimating the Effective Pressure on Patterned Wafers During STI CMP
3.3.1 Background
It is critical to establish a problem-free approach for STI CMP because STI
technology presents several advantages over the previous LOCOS technology such as
low junction capacitance, near zero-field encroachment and exceptional latch-up
immunity (Gan, 2000). The general structure and property of materials used in STI
technology has caused selectivity issues (i.e., oxide vs. nitride removal rates), nitride
erosion and trench oxide dishing. The aforementioned problems are generally associated
with the overall material properties (i.e., Young’s modulus) of the various STI layers, as
well as variations of local removal rates resulting from the effects of patterned structures
on the actual wafer pressure experienced during CMP.
Patterned wafers pose uniformity problems due to inconsistent planarization times
resulting from variations in die-level pattern density. It is known that for a set of identical
CMP process conditions and wafers with no variations in pattern density (i.e., uniform
and repeated patterns), more material is removed from a wafer with a lower pattern
density than from one with a higher pattern density. When considering a wafer with
significant variations in pattern density, typical polishing processes yield dramatic
variations in local removal rate (Tugbawa et al., 2001). As a result, determining local and
global removal rates becomes difficult, especially when considering that little is known
156
about the contact mechanisms at the pad–wafer interface. This limitation reduces the
capability of accurately determining the actual pressure experienced by the structures on
the wafer surface.
This study attempts to determine the effective pressure (i.e., the actual pressure
exerted on the structures of a patterned wafer, also known as the envelop pressure) during
STI CMP through a series of controlled temperature STI polishes. Using removal rate
results in conjunction with a simplified Langmuir-Hinshelwood kinetics mechanism for
material removal, this study derives the effective pressure experienced for STI wafers
ranging in pattern densities of 10 to 90 percent (Li et al., 2003).
3.3.2 Experimental Approach
The experiments performed for this study were done at the SNL and incorporated the
use of the SpeedFam IPEC-472 polisher described in Chapter 2.2.
The STI wafers used in the study had pattern densities of 10, 50 and 90 percent and
did not exhibit any die level pattern density variation. On the primary platen, polishing
experiments were performed in-situ at a conditioning pressure of 0.5 PSI. Cabot’s D7300
fumed silica slurry (approximately 12.5 percent by weight) was used in conjunction with
a Rohm and Haas IC-1400 K-grooved pad. The slurry flow rate was maintained at 270
cc/min for all tests and the slurry pH was approximately 11. Polishing tests were done at
applied wafer pressures of 3 and 7 PSI with a back-pressure of 0.2 PSI. Platen and carrier
speeds were set at 30 RPM. The polishing time for all experiments was 90 seconds.
157
All polishing conditions were repeated at platen temperatures of 10, 23, 35 and 45°C.
The primary platen temperature was controlled using the polisher’s internal heat
exchanger system for platen heating and an external chiller for platen cooling (described
in Chapter 2.2.3). The pad surface temperature was monitored prior to and during each
polish using the IR camera system described in Chapter 2.3.2. Before polishing, the pad
temperature was monitored until a steady state temperature was reached for at least 2
minutes. Pad surface temperature measurements during polishing were acquired using the
technique described in Chapter 2.2.3.
On the secondary platen (intended for buffing), wafer pressure was set to 5 PSI with
the carrier and platen rotating at 10 and 100 RPM, respectively. The buffing step was 30
seconds long and involved the use of Fujimi’s Surfin SSW1 pad and ultra-pure water.
Following each polish, wafers were mechanically scrubbed using PVA brush rollers on
an OnTrak DSS-200 scrubber. Silicon dioxide films were measured for pre- and post
thicknesses using a KLA-Tencor UV-1250 ellipsometer.
All of the STI wafers used in this study began with 100 Å of a thermally grown pad
oxide on a p-type silicon substrate. This was then followed by a 1500 Å silicon nitride
deposition. All wafer sets were then patterned and etched to obtain a trench depth of 3100
Å at pattern densities of 10, 50 and 90 percent. The wafers were then subjected to a
sidewall oxide layer growth of 250 Å via dry oxidation. This was followed by high-
density plasma (HDP) oxide trench fill of 10000 Å. As mentioned before, the reticles
used for the wafers in this study exhibited no variation in oxide density on the die and
158
wafer level for a given pattern density set (i.e., 10, 50 or 90 percent). This reduced the
possibility for variation in local planarization times on the wafer and die level.
3.3.3 Results and Discussion
Due to the thermal dependence of the Langmiur-Hinshelwood removal rate model
used in this investigation (this model will be described in greater detail in Chapter 5), the
first step towards determining the effective pressure of patterned wafers during CMP was
to ensure that process temperature was independent of pattern density (Li et al., 2003)
Based on the temperature results obtained from polishing experiments for each of the
pattern density sets, the calculated apparent activation energy, E, indicated no
dependence on pattern density. Table 3.2 shows the E values for all three pattern density
sets and it can inferred that the standard error in the activation energies is no more than
2.6 percent. This indicates that despite a nine-fold increase in pattern density (i.e., from
10 to 90 percent), the thermal variations during polishing were not impacted by the
increase in wafer topography. As a result, it can be assumed that there exists only one
apparent activation energy to describe the polishing tests from this study (approximately
0.18 eV) (Sorooshian et al., 2004).
By assuming a single E for this process and using the constants for HDP oxide for all
other necessary terms in Eqn. (1.14), a root finding technique was used to calculate the
effective pressure values for all pattern density polishes at platen temperatures of 10, 23,
35 and 45°C (the values in Tables 3.3 through 3.6 represent an average of four polishes).
159
Table 3.2: Apparent activation energy values for HDP filled STI wafers of variable pattern density
Table 3.3: Derived effective pressure values for STI polishes at a platen temperature of approximately 10°C. The values represent an average of four individual polishing experiments
Table 3.4: Derived effective pressure values for STI polishes at a platen temperature of approximately 23°C. The values represent an average of four individual polishing experiments
Pattern Density
Apparent Activation Energy (eV)
Standard Deviation (eV)
10% 0.172 0.01850% 0.172 0.06190% 0.182 0.087
Pattern Density
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 3 PSI
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 7 PSI
10% 8.15 ± 1.31 13.37 ± 2.3650% 5.12 ± 0.58 10.57 ± 1.3490% 2.90 ± 0.60 8.03 ± 0.65
Pattern Density
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 3 PSI
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 7 PSI
10% 8.01 ± 1.36 15.21 ± 4.8950% 4.64 ± 0.34 11.42 ± 0.9490% 3.50 ± 0.17 8.65 ± 0.67
160
Table 3.5: Derived effective pressure values for STI polishes at a platen temperature of approximately 35°C. The values represent an average of four individual polishing experiments
Table 3.6: Derived effective pressure values for STI polishes at a platen temperature of approximately 45°C. The values represent an average of four individual polishing experiments
Results from Tables 3.3 through 3.6 are summarized as follows:
• Effective pressure values do not represent a perfect contact mechanism between
the wafer and pad (i.e., the product of expected contact area and derived effective
pressure does not match the applied wafer pressure). This is to be expected
considering the multitude and complexity of interactions at the pad-wafer
Pattern Density
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 3 PSI
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 7 PSI
10% 8.58 ± 1.47 15.77 ± 1.9150% 4.66 ± 1.94 11.98 ± 1.1090% 3.66 ± 0.18 8.96 ± 0.74
Pattern Density
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 3 PSI
Derived Effective Pressure (PSI) at an Applied Wafer Pressure of 7 PSI
10% 12.73 ± 0.35 17.80 ± 0.5650% 7.96 ± 0.14 14.14 ± 0.4590% 4.91 ± 0.06 10.19 ± 0.26
161
interface during CMP. Factors such as interfacial fluid pressure, pad grooving and
process tribology could be some of the main causes for such deviations from an
ideal contact situation between the pad and wafer (Shan et al., 2000; Vlassak et
al., 2004; Zhou et al., 2002).
• Effective pressure converges to the applied wafer pressure as pattern density
increases. As expected with an increase in pattern density, more patterned
structures come into contact with the pad during polishing thus increasing the area
of contact and reducing the pressure to the applied processing value.
• As the platen temperature increases from 10 to 45°C, effective pressure values for
a given pattern density and applied wafer pressure have an increasing trend.
Although the average increase in effective pressure for all the conditions in Tables
2 through 5 is approximately 31 percent, the slight increase can be explained by
considering the effect of heat on pad properties during CMP. Figure 3.17 shows
results from a DMA analysis of an as-received IC-1400 K-grooved pad. The
flexural storage modulus of the pad decreases by approximately 30 percent (from
93 MPa to 65 MPa) as the pad temperature is increased from 10 to 45°C. Since
flexural storage modulus is a means of describing pad softening, it is suspected
that the observed softening allows for a more aggressive conditioning of the pad
surface, thus leading to greater asperities. This in turn, is believed to cause a drop
162
in the contact area at the pad-wafer interface, thereby creating the shift in the
derived effective pressure.
Figure 3.17: Flexural storage modulus results for as-received IC-1400 K-groove pad. Results were taken at a sampling frequency of 10 Hz
The effective pressure values derived from the above model present some insight
towards the actual prediction of the pressure occurring during CMP for wafers with
patterned structures. The main result of this study was that, regardless of applied wafer
pressure and platen temperature, the ratio of the derived effective pressure to applied
wafer pressure was relatively consistent. Ratios for all patterned wafers studied were
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50Pad Temperature (°C)
Flex
ular
Sto
rage
Mod
ulus
(MP
a)
163
approximately 2.2, 1.7 and 1.3 for 10, 50 and 90 percent density wafers respectively. The
stability of these ratios indicated that in cases of a five-fold (i.e., from 10 percent to 50
percent) or nine-fold increase in pattern density (i.e., from 10 percent to 90 percent), the
effective pressure experienced during polishing was not impacted by the pattern density
in a proportionate manner. This result can be a critical contribution in establishing
possible contact mechanisms between the pad and wafer during CMP. Furthermore, with
recent efforts in modeling CMP removal rates and uniformity with blanket and patterned
wafers, the results from this study can provide insight towards initial pressure estimates
for application in such models
3.3.4 Concluding Remarks
This study presents a first generation approximation of the effective pressure
experienced by STI patterned wafers during CMP. Using a simplified Langmuir-
Hinshelwood kinetics mechanism for ILD removal, results from a series of temperature
controlled HDP-filled STI polishes (pattern densities of 10, 50 and 90 percent) indicated
that process temperature was independent of pattern density, thus implying that any
observed differences in removal rate should be a result of pressure differences among
wafers with various pattern densities. As a result of this, a root finding technique enabled
the calculation of effective pressures from the removal rate mechanism used in this study.
Results showed that regardless of applied wafer pressure and platen temperature, the ratio
of the derived effective pressure to applied wafer pressure was relatively consistent. The
164
stability of these ratios indicated that in cases of a five-fold (i.e., from 10 percent to 50
percent) or nine-fold increase in pattern density (i.e. from 10 percent to 90 percent), the
effective pressure experienced during polishing was not impacted by the pattern density
in a proportionate manner. These findings are believed to have significant implications in
all CMP processes where shear force needs to be controlled or minimized (i.e., for copper
or low-k applications) for a wide range of pattern densities.
165
CHAPTER 4 – IMPACT OF TOOL KINEMATICS, PAD GEOMETRY AND TEMPERATURE ON THE REMOVAL RATE AND PROCESS TRIBOLOGY DURING ILD CMP
4.1 Motivation
The Freudenberg pad study was developed to provide a complete understanding and
characterization of ILD CMP with respect to changes in pad grooving, pad thickness,
platen set point temperature, slurry flow rate and kinematic process conditions. The
impact of these parameters was investigated with respect to variations in material
removal rate, changes in pad temperature as a function of changing p × V, changes in
mean COF as a function of pad temperature and the tribological mechanisms occurring
during each condition.
One of the primary highlights of this study was to understand the effect of platen set
point temperature on material removal rate and specifically developing an understanding
of the competing thermo-chemical and mechanical involved in the ILD CMP process.
The analyses regarding this aspect of the Freudenberg pad study is presented in Chapter 5
and will apply a new removal rate model based on flash heating to further describe the
above effects.
166
4.2 Tribology
By definition, tribology is the study of friction, wear and lubrication at interacting
surfaces in relative motion (Merriam Webster Dictionary, 2005). One of the origins of
tribology began in 1886 by Osborne Reynolds. Reynolds began his study of tribology by
developing equations for a flooded bearing with no lubricant flow out of either end of the
bearing. Reynold’s observed that the action of the lubricant surrounding the rotating shaft
creates a fluid pressure buildup via the pulling action of the fluid in the bearing contact
region. Assuming an incompressible fluid (i.e., the fluid density ρ is constant), Reynolds
defined the fluid flow as
( ) )(126)(633
obbobo vvuux
hxhuu
yph
zxph
x−+−
∂∂
+∂∂
−=
∂∂
∂∂
+
∂∂
∂∂
µµ (4.1)
where µ is the bulk fluid viscosity, h is the fluid film thickness, xp
∂∂ and
zp
∂∂ are the
pressure gradients, ua and va are the lower surface velocity components, and ub and vb
represent the upper surface velocity components. It should be noted that Eqn. (4.1) is
derived by the simplification of the Navier-Stokes equations. In the above equation, the
first two terms are named the Poiseuille terms and are used to define the net flow rates
caused by pressure gradients in the area of lubrication. The terms on the right hand side
of Eqn. (4.1) are called the Couette terms. The Couette terms describe the net flow rates
167
caused by surface velocities. On the right hand side of Eqn. (4.1), the first three
expressions describe the net fluid flow rate resulting from the compressive action at the
bearing surface. The final term in Eqn. (4.1) is an expression represents the net fluid flow
rate caused by local compression (Szeri, 1999).
In order to reach the above form of the Reynolds equation, several assumptions must
be made. The assumptions are as follows:
• Incompressible and Newtonian fluid
• Using dimensional scaling, the length scale of the fluid film thickness is
negligible
• Gravitational and inertial forces are neglected
• No-slip boundary condition at the liquid-solid or gas-solid interface
When the above conditions are applied to Navier-Stokes equations, the resulting
equation is called the Reynolds equation, Eqn. (4.1). Through this derivation, a non-
dimensionless term called the Reynolds number is acquired and it describes the ratio of a
fluid’s inertial forces by a fluid’s viscous forces (Bird et al., 2002). The Reynolds number
is often used to characterize fluid flow as either laminar (Re ≤ 2200) or turbulent (Re >
2200) based on its absolute value. Equation (4.2) is the simplified expression for the
Reynolds number.
2
Re
⋅⋅
=LhLu
µρ (4.2)
168
In the above equation, u is the fluid velocity, µ is the fluid viscosity, ρ is the fluid
density, h is the fluid film thickness. As seen in Chapter 2, the tool scaling parameter for
platen speed is based on Reynolds number. This is a result of the relationship that can be
established between the bearing analysis done by Reynolds and CMP. In the simplest
sense, one can relate the rotating bearing, entrained fluid and bearing casing in the
Reynolds model to the wafer, slurry and pad used in CMP respectively. Using the
Reynolds number as a scaling parameter in CMP tool design requires one to define the
parameter of h and u in Eqn. (4.2) as the fluid film thickness between the pad and wafer
and relative pad-wafer sliding velocity, respectively (Sundararajan et al., 1999).
Based on the Reynolds number justification of tool scaling, it is possible to evaluated
the tribological effects of CMP through multiple characterization techniques.
4.2.1 Stribeck-Gumbel Curve
The Stribeck curve is used to characterize the three various lubrication regimes
encountered during CMP at the pad-wafer interface. The Stribeck curve is based on the
observed frictional trends of a set of experiments involving a shaft within a lubricated
journal bearing. During the study, an applied load was added to one end of the shaft while
the shaft spun in a single direction within the isolated journal bearing. A schematic of this
set-up can be seen in Fig. 4.1. As the shaft rotated, the shear force of the lubricant
between the shaft and wall of the journal bearing was taken along with the COF. Once
again, COF is defined by the ratio of the shear force to the normal force of the set-up.
169
By definition the Stirbeck curve is constructed by plotting the COF against the
Hersey number shown in Eqn. (4.3).
pVnumberHersey µ⋅
= (4.3)
In Eqn. (4.3) V is the relative linear velocity of the shaft to the journal bearing, µ is
the lubricant viscosity and p is the applied pressure on the shaft. Note that the Hersey
number has units of length.
Figure 4.1: Journal bearing-shaft set-up for Stribeck model
A typical Stribeck curve is depicted in Fig. 4.2. As seen from the figure, the Stribeck
curve exhibits three distinctive regions of lubrication. Going from left to right on the
curve, the first segment appears nearly horizontal and indicates no change in COF with
respect to an increasing Hersey number. This segment is known as the boundary
lubrication regime and it describes direct body contact between the shaft and journal
bearing. The second segment, which occurs at the onset of the curve and decreases in a
v
vshaft
bearing
load
v
vshaft
bearing
load
170
steep manner, represents the partial lubrication regime. Partial lubrication describes a
partial levitation of the shaft from the journal bearing. The final segment of the Stribeck
curve (furthest right) is known as the hydrodynamic lubrication regime and describes a
shaft that is completely separated from the journal bearing by a film of lubricant.
Hydrodynamic lubrication often occurs as a result of high shaft velocities and low
applied pressures (Ludema, 1996).
Figure 4.2: Stribeck curve for journal bearing-shaft model
To relate the Stribeck curve to the lubrication mechanisms of CMP, the correlative
arguments made between the bearing experiments in the Reynolds model and CMP must
be used again. Figure 4.3 shows an example of a typical Stribeck curve used for CMP
0.001
0.01
0.1
1
1.0E
-03
1.0E
-02
1.0E
-01
1.0E
+00
Sommerfeld Number 'So'
Coe
fficie
nt o
f Fric
tion
'COF
'
Asperity contact
Partial contact(mixed lubrication)
Hydrodynamic Lubrication
0.001
0.01
0.1
1
1.0E
-03
1.0E
-02
1.0E
-01
1.0E
+00
Sommerfeld Number 'So'
Coe
fficie
nt o
f Fric
tion
'COF
'
Asperity contact
Partial contact(mixed lubrication)
Hydrodynamic Lubrication
171
systems (Stribeck-Gumbel curve). Similar to the Stribeck curve used in the journal
bearing system, the CMP Stribeck curve is identical in form but it is plotted using the
Sommerfeld number as opposed to the Hersey number on the x-axis. This change will be
discussed in the next section. Going from left to right on Fig. 4.3, the same three
lubrication regimes are observed once again, however the defined contact mechanisms
are different. The boundary lubrication regime describes direct contact between the pad,
slurry particle and wafer. In such a scenario, the height of the fluid film thickness, h,
between the pad and wafer is approximately zero. In CMP applications, operating in
boundary lubrication allows for easier process control since there is very little COF
variation with respect to the So. The drawback to operating in boundary lubrication is
excessive pad wear due to direct body contact between the wafer and pad.
Figure 4.3: Stribeck-Gumbel curve for CMP applications
0.001
0.01
0.1
1
1.0E
-03
1.0E
-02
1.0E
-01
1.0E
+00
Sommerfeld Number 'So'
Coe
ffici
ent o
f Fric
tion
'CO
F'
Boundary Lubricationh ~ Ra
h ~ 0
h >> Ra
Partial Lubrication
Hydrodynamic Lubrication
0.001
0.01
0.1
1
1.0E
-03
1.0E
-02
1.0E
-01
1.0E
+00
Sommerfeld Number 'So'
Coe
ffici
ent o
f Fric
tion
'CO
F'
Boundary Lubricationh ~ Ra
h ~ 0
h >> Ra
Partial Lubrication
Hydrodynamic Lubrication
172
The partial lubrication regime describes partial contact between the pad, slurry
particles and wafer. In this situation, h is approximately equal to the mean surface
roughness of the pad, Ra. Operating in partial lubrication has the advantage of minimizing
pad wear, however it comes at the cost of difficult process control.
The hydrodynamic lubrication regime (furthest left) represents no contact between the
wafer and pad. In this case, h is much larger than the Ra of the pad. This mechanism
seldom occurs during CMP since it requires excessively high flow rates and
unconventional kinematic conditions to allow for slurry to entrain within the pad-wafer
interface.
4.2.2 Sommerfeld Number
As mentioned earlier, Fig. 4.3 applies the Sommerfeld number, as opposed to the
Hersey number for plotting the Stribeck curve for CMP systems. The primary issue with
the Hersey number was the fact that it resulted in units of inverse length. Since the CMP
set-up at the IPL involved scaling down an industrial grade polisher, it was critical that
the scaling parameters used in tool construction and analysis be dimensionless. Since the
Hersey number possessed units of inverse length a slight mathematical modification was
performed on the parameter to make it dimensionless. The new parameter, also known as
the Sommerfeld number, So, is defined as
173
effpVSo
δµ
⋅⋅
= , (4.4)
where V is the pad-wafer sliding velocity, p is the applied wafer pressure, µ is the slurry
viscosity and δeff is the effective fluid film thickness between the pad and wafer (Moore,
1975). The resulting plot of COF versus So (Fig. 4.3) is known as the Stribeck-Gumbel
curve (Ludema, 1996).
The new parameter of δeff, which was used to non-dimensionalize the Hersey number,
can be further defined as
aeff R⋅= αδ , (4.5)
where α is a parameter that is calculated to define the overall percentage of ‘up-area’
versus ‘down area’, or groove area, of a polishing pad. Equation 4.6 provides a further
definition of α.
PitchWidthGroovePitch −
=α (4.6)
As it can be inferred from the definition, α varies for each polishing pad groove type
and can be calculated using scanning profilometry or approximated using measurements
by electronic calipers. By definition, a flat polishing pad has an α=1 and all other grooved
pads have α less than one.
It should be noted that the calculation of δeff neglects the fluid layer within the overall
groove area of the pad. The reason this is not accounted for is based on the fact that the
entrained slurry within pad grooving is not suspected to contribute to wafer polishing or
friction during CMP. To fully characterize the fluid film thickness at the pad-wafer
interface during CMP, several parameters must be considered including pad porosity, pad
174
compressibility, pad-wafer sliding velocity, applied wafer pressure, slurry viscosity, etc.
(Thakurta et al., 2000; Runnels et al., 1994; Mullany et al., 2003; Lu et al., 2000; Levert
et al., 1997). Since the capabilities of measuring some of these parameters falls short of
what is needed, an approximation to the fluid film thickness was suitable for the purposes
of this research.
4.2.3 Coefficient of Friction
Frictional data was taken during polishing at a sampling frequency of 1000 Hz.
Following a one-minute polishing experiment, 60,000 data points would be taken on
average. Friction data acquisition would be initiated just following wafer contact with the
pad and would ensue until the desired polish time. Following each polish, the frictional
data would be averaged and the resulting value would be calculated into a mean COF
value for a certain run. These values would then be used to plot Stribeck-Gumbel curves
for a specific experimental setup to determine the lubrication regime that was occurring
during CMP.
4.3 Freudenberg Pad Study
The Freudenberg pad study entailed the complete investigation of the effect of pad
groove design and pad thickness on the frictional and kinetic attributes of thermal oxide
175
CMP over a wide range of platen temperatures. Polishing pads were provided by
Freudenberg non-wovens for the sole purposes of this study. Parameters considered in
this study included:
• Pad Groove Design – Flat, XY-groove and Perforated
• Pad Thickness – 1.39 and 2.03-mm
• Platen Set Point Temperatures – 13, 24, 33 and 43°C
• Slurry flow rate – 40 and 120 cc/min
• Wafer Pressure – 2, 4 and 6 PSI
• Pad-wafer sliding velocity – 0.32, 0.64, 0.96 m/s
The overall objectives of this study were as follows:
1. Determine the effect of pad grooving, thickness and temperature on blanket
thermal oxide removal rates and COF
2. Determine the effect of slurry flow rate on blanket thermal oxide removal rates
and COF
3. Determine the apparent activation energy for each process set (i.e., pad groove
and thickness). This is to establish if variations in pad grooving or pad thickness
generate distinct variations in apparent activation energy of the polish process.
176
Assuming that different consumable sets (i.e., pad material or slurry type) will
yield dissimilar activation energies as a result of their’ material properties, it
would be expected that variations in pad grooving or thickness would not create
significant variations.
4. Calculate fitting parameters for predicting removal rates using the newly
developed Langmuir-Hinshelwood model. These results will be discussed in
Chapter 5.
5. Determine the effect of pad grooving, thickness and temperature on the
lubrication mechanism of the process.
6. Determine the effect of slurry flow rate on the lubrication mechanism of the
process.
7. Determine any possible correlations involving removal rates or process tribology
to the dynamic material properties of the pads used.
The design of experiment involved in study took into account six factors (applied
wafer pressure, sliding velocity, platen set point temperature, pad groove type, pad
thickness and slurry flow rate). Of the six, five were quantitative factors and one (pad
groove type) was a qualitative factor. From the analysis, two responses were acquired
177
removal rate and COF. Due to the overwhelming number of input and output parameters,
the results from the Freudenberg study have been divided such that logical comparisons
can be made among the results. Results presented in the subsequent sections will
primarily focus on results taken at a platen temperature of 24°C (room temperature),
since these testing conditions are considered more conventional in industry and proved
more consistent during experimentation. Removal rate and thermal results recorded at all
platen temperatures will also be discussed, however they will mainly be included in the
modeling portion of this research in Chapter 5. This chapter will present several sets of
removal rate and Stribeck-Gumbel curves for the study in question, in addition to
accompanied regression analysis which will summarize the main factors effecting the
experimental results shown. Coupled together, the raw data as well as the statistical
results will provide physical explanations of the results.
4.3.1 Experimental Approach
The CMP experiments performed for this study were done at the IPL and
incorporated the use of the scaled polisher described in Chapter 2.1. The acquisition of
COF data for this study have been described in Chapter 2.1.6 and 4.2.3. Platen
temperatures for this study were controlled using the technique described in Chapter
2.1.9.
The IR camera described in Chapter 2.3.2 was used to record the pad surface
temperature prior to and during polishing. As described in that section, the mean process
178
temperature of a polish was calculated as the average value of the ten temperature points
shown in Fig. 2.23.
Wafers used for the CMP experiments were 100-mm diameter silicon dioxide wafers.
The polishing time per wafer was 90 sec. Polishing experiments were run with in-situ
conditioning at a conditioner pressure of 0.5 PSI. Fujimi’s PL-4217 fumed silica slurry
(approximately 12.5 percent solid by weight with a pH of 11) was used with Freudenberg
pads of each type of groove and thickness described above. Polishing was done at slurry
flow rates of 40 and 120 cc/min. The following load and rotation rate conditions were
used:
• Pad-wafer sliding velocity = 0.32 m/s (40 RPM), Applied wafer pressure = 2, 4
and 6 PSI
• Pad-wafer sliding velocity = 0.64 m/s (80 RPM), Applied wafer pressure = 2, 4
and 6 PSI
• Pad-wafer sliding velocity = 0.96 m/s (120 RPM), Applied wafer pressure = 2, 4
and 6 PSI
All pressure/velocity conditions were run twice in order to assess data repeatability.
All polishing conditions were also run at initial platen set point temperatures of
approximately 13, 24, 33 and 43°C. It should be noted that the platen set point
temperature does not remain constant during polishing, but provides a desired initial
thermal condition for polishing experiments. Prior to polishing, the pad temperature was
179
monitored until a steady state temperature was reached for at least 2 minutes. As noted
above, the desired platen set point temperature is not the same as the actual temperature
that was recorded using IR during polishing. The set point temperature creates a general
variation in the thermal environment. Frictional heating induced by polishing causes the
local temperature to exceed the initial set point temperature.
180
4.3.2 Removal Rate as a Function of Tool Kinematics
Figures 4.4 through 4.15 are removal rate plots for ILD films as a function of tool
kinematics (i.e., applied wafer pressure and sliding velocity), as well as pad thickness and
process flow rate. Each set of data was taken under ambient conditions (approximately
24°C). Removal rates have been plotted by each independent velocity in order to
highlight the apparent linear dependence of removal rate with sliding velocity. This
phenomenon will be discussed in further detail in Chapter 5. Since there is some
difficulty associated with determining direct relationships between removal rate and the
multiple input factors from these figures, an interactive statistical regression analysis was
done.
The statistical analysis was completed using Cornerstone® software and involved the
application of the raw data to a 2-level interactive significance model. Table 4.1 presents
single and 2-level input effects in terms of their relative significance on the experimental
removal rate. Note that Table 4.1 shows the relative significance of these parameters in
ascending order, such that smaller values a more significant and larger values are less
significant. Also note that the R-squared value acquired from this regression analysis was
approximately 0.93, which indicates excellent confidence in the data.
From this table it is clear that removal rate is largely affected by the combined effect
of p × V. This result is to be expected considering the fact that p × V is the primary
mechanical force for material removal during CMP. As seen from Figs. 4.4 through 4.15,
a change in either applied wafer pressure or sliding velocity will cause a noticeable
181
change in removal rate. If one considers these results in conjunction with the flash
heating removal rate model proposed in Chapter 1.5.4, it can be concluded that the
primary driving force for material removal in ILD CMP for this study lies in the
mechanical rate constant, k2. Although both rate terms, k1 and k2, are functions of p × V,
the direct proportional relationship of p × V on k2 is much more significant than that of
k1.
Table 4.1: Statistical regression results for removal rate. Results are listed in ascending order, with the most significance results appearing at the top of the list
Parameter Relative SignificancePressure * Velocity 0.000E+00Groove * Thickness 0.000E+00Groove 2.331E-15Groove * Temperature 1.794E-12Groove * Velocity 8.360E-07Groove * Pressure 1.470E-02Thickness 1.542E-02Temperature * Thickness 1.683E-02Flow Rate * Velocity 1.036E-01Pressure * Thickness 2.858E-01Constant 3.243E-01Temperature 3.869E-01Pressure * Temperature 5.054E-01Temperature * Velocity 5.350E-01Flow Rate * Pressure 5.812E-01Thickness * Velocity 6.552E-01Pressure 6.593E-01Flow Rate * Thickness 6.739E-01Velocity 6.742E-01Flow Rate 9.506E-01Flow Rate * Groove 9.913E-01Flow Rate * Temperature 9.927E-01R-Squared 0.9274Adj R-Square 0.9231RMS Error 205.4110Residual df 458
Removal Rate
182
Figures 4.4 through 4.6 and Figs. 4.7 through 4.9 show the removal rates of the 1.39-
mm pads at slurry flow rates of 40 and 120 cc/min respectively. In both flow rate
situations, the XY-groove pad generated the highest respective removal rate at each p × V
combination. This was then followed by the flat pad and perforated pad, which showed
the lowest amount of material removal.
This observation, coupled with the information provided in Table 4.1 shows that pad
grooving is another primary factors in determining ILD removal rate. The impact of pad
grooving is shown to occur both singularly and in combination with pad thickness,
temperature, sliding velocity and applied wafer pressure. The underlying effect that
grooving may have on removal rate can stem from a number of factors including its
impacts on slurry transport, heat generation at the pad-wafer interface, and relative extent
of contact during CMP.
Figure 4.4: Removal rate plot for 1.39-mm thick Freudenberg flat pad at a polishing flow rate of 40 cc/min
183
Figure 4.5: Removal rate plot for 1.39-mm thick Freudenberg XY-groove pad at a polishing flow rate of 40 cc/min
Figure 4.6: Removal rate plot for 1.39-mm thick Freudenberg perforated pad at a polishing flow rate of 40 cc/min
184
Figure 4.7: Removal rate plot for 1.39-mm thick Freudenberg flat pad at a polishing flow rate of 120 cc/min
Figure 4.8: Removal rate plot for 1.39-mm thick Freudenberg XY-groove pad at a polishing flow rate of 120 cc/min
185
Figure 4.9: Removal rate plot for 1.39-mm thick Freudenberg perforated pad at a polishing flow rate of 120 cc/min
Figure 4.10: Removal rate plot for 2.03-mm thick Freudenberg flat pad at a polishing flow rate of 40 cc/min
186
Figure 4.11: Removal rate plot for 2.03-mm thick Freudenberg XY-groove pad at a polishing flow rate of 40 cc/min
Figure 4.12: Removal rate plot for 2.03-mm thick Freudenberg perforated pad at a polishing flow rate of 40 cc/min
187
Figure 4.13: Removal rate plot for 2.03-mm thick Freudenberg flat pad at a polishing flow rate of 120 cc/min
Figure 4.14: Removal rate plot for 2.03-mm thick Freudenberg XY-groove pad at a polishing flow rate of 120 cc/min
188
Figure 4.15: Removal rate plot for 2.03-mm thick Freudenberg perforated pad at a polishing flow rate of 120 cc/min
As mentioned before, pad grooving is a qualitative aspect in polishing. In order to
provide a more comprehensible view of how pad grooving impacts removal rate, Figs.
4.16 through 4.21 provide contour plots of experimental removal rate as a function of
applied wafer pressure and sliding velocity for each of the three pad groove types used in
the study, as well as the two varying pad thicknesses. For a given pad thickness, the
graphical results shown in these figures provide further evidence of the dependence of
removal rate on pad groove type. This is especially noticeable at low values of applied
wafer pressure and sliding velocity, as well as the specific case of the 1.39 mm pad
thickness (this may not be as obvious in Figs. 4.4 – 4.15). Discussion as to the impact of
pad grooving on the mechanical and chemical aspects of ILD CMP will be conferred in
Chapter 4.3.3.
189
Figure 4.16: Predicted removal rate (Å/min) contour plot for the Freudenberg perforated pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
Figure 4.17: Predicted removal rate (Å/min) contour plot for the Freudenberg flat pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
400
600
600
600
00
800
800
800
1000
1000
1000
1000
1200
1200
1200
1400
1400
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1600
1800 2000
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
600
600
800
800
800
800
000
1000
1000
1000
1200
1200
1200
1200
1400
1400
1400
1600
1600
18002000
p
190
Figure 4.18: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
Figure 4.19: Predicted removal rate (Å/min) contour plot for the Freudenberg perforated pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
400
400
600
600
600
600
00
800
800
800
1000
1000
1000
1000
1200
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1200
1400
1400
1400
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2000
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
400
00
600
600
600
800
800
800
800
1000
1000
1000
1000
1200
1200
1200
1400
1400
1600
1600
1800 2000
p
191
Figure 4.20: Predicted removal rate (Å/min) contour plot for the Freudenberg flat pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
Figure 4.21: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
600600
600
00
800
800
800
000
1000
1000
1000
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1400
1400
1400
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1800 2000
p
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6Pressure
800
800
1000
1000
1000
200
1200
1200
1200
1400
1400
1400
1400
1600
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1600
1800
1800
1800
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2000
2200
2200
2400 2600
p
192
As mentioned earlier, the XY pad resulted in the highest removal rate, followed by
the flat and perforated pads (1.39 mm pad only). To further establish the reason for
increased removal rate with the XY-groove pad, DMA results obtained for each of the
pad types studied showed that the XY-groove pad had the lowest rate of storage modulus
decrease over the range of polishing temperatures (approximately 1.85 MPa/°C).
Comparing this value to those of the flat and perforated pads, which resulted in decreases
of approximately 6.35 and 5.25 MPa/°C respectively, the XY-groove pad maintains
nearly 2.5 times greater rigidity during polishing. As mentioned in prior sections, greater
pad rigidity and hardness directly correlates to high removal rates during polishing, thus
corroborating the results found from Figs. 4.4 through 4.6 and Figs. 4.7 through 4.9.
At the other extreme, the perforated pad showed lower than expected removal rates (
1.39 mm pad only). This results may appear somewhat unconventional since the
perforated pad is expected to yield higher removal rates due to the pads pronounced
ability to transport slurry to the polishing interface (when compared to the flat pad). Upon
this note, it should be mentioned that the pads constructed for this study were not
identical to those used in conventional processing. Slight variations in grooving
dimension could lead to unexpected removal rate results. Furthermore, the relative scatter
associated with each groove type was highest for the flat and perforated grooving. This
could directly imply that a greater variation of slurry transport to the pad-wafer interface
was apparent for those two groove types thus effecting removal rate. This supposition is
also confirmed by the results shown in Table 4.1.
193
On a final note, Table 4.1 also indicated that platen set point temperature did not have
as great of an impact on removal rate. When compared to other polished films such as
copper, ILD is much less thermally sensitive, thus indicating a less chemically active
polishing process. The results from Table 4.1 confirm this in showing that the mechanics
involved in polishing have a more profound effect on ILD removal rate. In order to
further show the insensitivity of platen set point temperature on ILD removal rates from
this study Figs. 4.22 through 4.24 show contour removal rate plots for the 2.03 mm XY-
groove pad at platen set point temperatures of 17, 30 and 47°C respectively. When one
compares these three figures along with Fig. 4.18 (2.03 mm, XY-groove at 24°C), it is
evident that the variation in removal rate is not as significant as one would expect.
Figure 4.22: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min at 17°C. Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
400
400
600
600
600
00
800
800
800
1000
1000
1000
1000
1200
1200
1200
1400
1400
1400
1600
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1800
1800
2000
194
Figure 4.23: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min at 30°C. Note that velocity is reported in RPM and pressure is reported in PSI
Figure 4.24: Predicted removal rate (Å/min) contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min at 47°C. Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
200 400
400
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600
600
00
00
800
800
800
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1400
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40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
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3
3.5
4
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5
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6Pressure
2 00 400
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195
4.3.3 Tribological Mechanisms
Figures 4.25 through 4.72 are Stribeck-Gumbel curves for each set of experiments run
for this study. The figures are separated based on pad groove type, pad thickness and
slurry flow rate. Each figure contains a series of four Stribeck-Gumbel curves
representing the platen set point temperature conditions that were used during testing. It
should be noted that for all the plotted data in Figs. 4.25-4.72, the dependency of slurry
viscosity with temperature was accounted for (Geankoplis, 1993).
Results from each series of figures showed that the predominant tribological
mechanism during polishing was boundary lubrication. This was true regardless of pad
thickness, pad groove type, platen set point temperature or slurry flow rate. It should be
noted that based on some of the results, an argument could be made that some of the
polishing conditions generated hydrodynamic conditions (i.e., Figs. 4.29-4.40). These
special cases were observed with the flat pad only. Although the data may indicate such
hydrodynamic trends, the magnitude of COF data taken under those conditions is far too
great to implicate hydrodynamic mechanisms are occurring with the pad-wafer interface.
Based on this fact, it can be said that all the COF trends indicate boundary lubrication
conditions.
To lend a possible explanation for these trend variations, one must consider the
potential sources of error associated with acquiring COF data during experimentation.
The first point of error may be associated with the viscosity parameter included within
the So parameter. Although changes in viscosity with temperature have been accounted in
196
the analysis of this data, there still remains several points of uncertainty with regards to
this parameter. First, the viscosity values considered for calculating So in this study are
for that of water. It may be assumed that the variations of slurry viscosity with
temperature are very similar to those observed for water, however, slight discrepancies
may exist between the two fluids which could drive data into showing different trends.
Moreover, several studies have shown that slurry viscosity changes with shearing (Levy
et al., 2003). This may also alter values enough to create different trends.
Another possible source of error involves the effective fluid film thickness parameter,
δeff. The error associated with this parameter lies in its calculation, which assumes that the
wafer and the average of the pad asperity height are always in contact (thus not
accounting for any potential slurry film thickness at the interface).
The final source of error associated with the Stribeck-Gumbel curves lies in the
experimental error associated with COF acquisition during testing. Discontinuities in
slurry flow (via clogging of the slurry line) or human contact with the isolation table or
polisher can both cause changes in friction table movement thus impacting the overall
COF for a polish. Although these events occur very rarely, their occasional incidence can
cause the most significant sources for error.
As in the case of removal rate, the COF data acquired from this study was also
analyzed statistically using Cornerstone® software. The modeling specifications for COF
were identical to those used for removal rate. Table 4.2 presents single and 2-level input
effects in terms of their relative significance on the experimental COF. Once again, note
197
that Table 4.2 shows the relative significance of these parameters in ascending order,
such that smaller values a more significant and larger values are less significant.
Table 4.2: Statistical regression results for COF. Results are listed in ascending order, with the most significance results appearing at the top of the list
Parameter Relative SignificanceGroove * Pressure 7.772E-16Groove * Thickness 7.437E-10Groove * Temperature 1.122E-05Groove * Velocity 1.742E-04Groove 1.120E-03Pressure * Thickness 7.326E-03Temperature * Velocity 1.295E-01Velocity 1.682E-01Flow Rate * Temperature 1.942E-01Flow Rate 2.030E-01Flow Rate * Thickness 2.244E-01Pressure * Velocity 3.502E-01Temperature * Thickness 4.039E-01Flow Rate * Velocity 5.750E-01Flow Rate * Groove 6.149E-01Thickness 6.417E-01Pressure * Temperature 7.703E-01Flow Rate * Pressure 8.231E-01Pressure 8.821E-01Temperature 8.912E-01Thickness * Velocity 9.838E-01Constant 9.842E-01R-Squared 0.4552Adj R-Square 0.4231RMS Error 0.0578Residual df 458
COF
198
It should be noted that the R-squared value acquired from the COF regression
analysis was approximately 0.46, which indicates that the data acquired was not as stable
and repeatable as one would desire. The reasons for such a results are described above.
Results from Table 4.2 show that pad grooving largely influences COF. This result is
consistent with those found for removal rate. One argument as to why pad grooving has
such a large impact on COF is that COF itself, is extremely sensitive to the interactions of
the wafer, pad and slurry. By altering the grooving of a pad, one also alters the
interactions that occur at this pad-slurry-wafer interface. This occurs as a result of the
grooves ability to change in slurry transport and consequently the extent of interfacial
lubrication.
Although pad grooving can not be ‘parameterized’ with in the flash heating model of
Chapter 1.5.4, one can still make an argument as to the relative impact of pad grooving
on the mechanical or chemical rate constants of the model. It may be argued that since
COF has a proportional relationship with removal rate, then the factors influencing COF
may also have a direct impact on removal rate. If one looks back to the flash heating
model, it may be inferred that COF, similar to p × V, has a direct influence on the
mechanical rate constant (k2) of the removal rate model. From this one can presume that
the effect of pad grooving, once again, has a more direct impact on the mechanical aspect
of ILD CMP as compare to the chemical aspect.
The above assumptions may also be corroborated with past studies that have
determined that ILD CMP processes are primarily driven by the mechanical actions
involved in the process and not the chemistry (Oliver et al., 2004). To provide a graphical
199
interpretation of the above stated influence of pad grooving on COF, Figs. 4.25 through
4.30 show contour plots of experimental COF as a function of applied wafer pressure and
sliding velocity for each of the three pad groove types used in the study, as well as the
two varying pad thicknesses.
For a single pad thickness, it is clear that pad grooving has a noticeable affect on COF
as is indicated by the varying contour lines. From the figures one can also notice that the
combination of pad thickness coupled with pad grooving generally yields distinct COF
trends per combination. Coupling the above graphical results along with results generated
in Table 4.2, several factors that may be considered as possible factors in effecting COF
and removal rate results can be eliminated. For example, one would expect factors such
as slurry flow rate or platen set point temperature alone to have an effect on these output
parameters, however Tables 4.1 and 4.2 indicate that these two factors have very little
impact. From this one could suspect that pad grooving is actually impacting multiple
predictors thus creating a macro change in the system. This concept is shown in Tables
4.1 and 4.2 as pad grooving is shown to be significant in several combined effects.
Dissociation of these effects would involve more in depth analysis of the frictional
signals (fast Fourier transforms, FFT), which will be done in the future.
200
Figure 4.25: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min
Figure 4.26: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min
201
Figure 4.27: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min
Figure 4.28: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min
202
Figure 4.29: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min
Figure 4.30: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min
203
Figure 4.31: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min
Figure 4.32: Stribeck-Gumbel curves for 1.39-mm flat pad at a platen set point temperature of 43°C and a slurry flow rate of 120 cc/min
204
Figure 4.33: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min
Figure 4.34: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min
205
Figure 4.35: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min
Figure 4.36: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min
206
Figure 4.37: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min
Figure 4.38: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min
207
Figure 4.39: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min
Figure 4.40: Stribeck-Gumbel curves for 2.03-mm flat pad at a platen set point temperature of 43°C and a slurry flow rate of 120 cc/min
208
Figure 4.41: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min
Figure 4.42: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min
209
Figure 4.43: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min
Figure 4.44: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min
210
Figure 4.45: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min
Figure 4.46: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min
211
Figure 4.47: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min
Figure 4.48: Stribeck-Gumbel curves for 1.39-mm XY-groove pad at a platen set point temperature of 43°C and a slurry flow rate of 120 cc/min
212
Figure 4.49: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min
Figure 4.50: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min
213
Figure 4.51: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min
Figure 4.52: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min
214
Figure 4.53: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min
Figure 4.54: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min
215
Figure 4.55: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min
Figure 4.56: Stribeck-Gumbel curves for 2.03-mm XY-groove pad at a platen set point temperature of 43°C and a slurry flow rate of 120 cc/min
216
Figure 4.57: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min
Figure 4.58: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min
217
Figure 4.59: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min
Figure 4.60: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min
218
Figure 4.61: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min
Figure 4.62: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min
219
Figure 4.63: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min
Figure 4.64: Stribeck-Gumbel curves for 1.39-mm perforated pad at a platen set point temperature of 43°C and a slurry flow rate of 120 cc/min
220
Figure 4.65: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 13°C and a slurry flow rate of 40 cc/min
Figure 4.66: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 24°C and a slurry flow rate of 40 cc/min
221
Figure 4.67: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 33°C and a slurry flow rate of 40 cc/min
Figure 4.68: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 43°C and a slurry flow rate of 40 cc/min
222
Figure 4.69: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 13°C and a slurry flow rate of 120 cc/min
Figure 4.70: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 24°C and a slurry flow rate of 120 cc/min
223
Figure 4.71: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 33°C and a slurry flow rate of 120 cc/min
Figure 4.72: Stribeck-Gumbel curves for 2.03-mm perforated pad at a platen set point temperature of 43°C and a slurry flow rate of 120 cc/min
224
Figure 4.73: Predicted COF contour plot for the Freudenberg perforated pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
Figure 4.74: Predicted COF contour plot for the Freudenberg flat pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
0.3080.31
0.31
0.31
0.312
0.312
0.312
.312
0.314
0.314
0.314
0.316
0.316
0.318.32
p
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure0.240.26
0.26
0.28
0.28
0.28
0 .3
0.3
0.3
0.3
0 .32
0.32
0.32
0.32
0 .34
0.34
0.34
0.340.36
0.36
0.36
0.38
0.38
0.4
225
Figure 4.75: Predicted COF contour plot for the Freudenberg XY pad (2.03 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
Figure 4.76: Predicted COF contour plot for the Freudenberg perforated pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
355
0 .36
0.36
365
0.365
0.365
.37
0 .37
0.37
0.37
0.375
0.375
p
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
0 .3
0.3
0.305
0.305
0.305
0 .31
0.31
0.31
0.31
315
0.315
0.3150.315
0 .32
0.320.32
0.32325
0.3250.325 0.325
p
226
Figure 4.77: Predicted COF contour plot for the Freudenberg flat pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
Figure 4.78: Predicted COF contour plot for the Freudenberg XY pad (1.39 mm) at a flow rate of 120 cc/min (room temperature). Note that velocity is reported in RPM and pressure is reported in PSI
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure
0.20.22
0.22
0.22
0 .24
0.24
0 .24
0.24
0 .26
0.26
0.26
0.26
0.28
0.28
0.28
0.3
0.3
0.32
40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120Velocity
2
2.5
3
3.5
4
4.5
5
5.5
6
Pressure 28
0.28
0.28
0.28
0.285
0.285
0.285
0.285
0.29
0.29
0.29
0.295
0.295
0.3
p ( ), p
227
4.3.4 IR Process Temperature as a Function of Tool Kinematics
4.3.4.1 1.39-mm Pad Thickness
This portion of the study focused on the extent of heat generation as a result of using
variable pad grooving and pad thickness for CMP. The analysis looked at the amount of
heat generation from an initial pad temperature ranging from approximately 20 to 25°C.
This analysis would enable one to understand the impacts that pad grooving and pad
thickness could have on heat generation, adsorption and dissipation during polishing as a
function of tool kinematics (i.e., p × V).
Figures 4.79 through 4.81 show the mean IR temperature readings for all three pad
groove types for a pad thickness of 1.39-mm and flow rates of 40 and 120 cc/min. The
observed thermal readings are plotted per polish at each individual pressure and velocity
condition. First, if one focuses on a single pad and observes the variations in temperature
rise for each slurry flow rate condition (40 and 120 cc/min), it can be inferred that the
rises in temperature are slightly higher for 40 cc/min at a p × V value of 39 kPa-m/s. The
mean difference in temperature rise between the two flow rates at 39 kPa-m/s is
approximately 1.8°C. This slight rise can directly be associated to the amount of slurry on
the pad at the high sliding velocity associated with the 39 kPa-m/s condition (120 RPM).
At this high sliding velocity, the slurry distributed on the pad discharges off the pad at a
greater rate, thereby limiting the amount of slurry reaching the interfacial contact region.
Based on this, a lower flow rate condition (i.e., 40 cc/min) would reduce the amount of
228
slurry reaching the pad-wafer interface thus creating a drier contact mechanism at the
polishing interface. This drier contact effect would consequently create greater heat and
result in a rise of temperature. Though this thermal rise is not truly significant in
magnitude, it still validates the role that slurry plays in the thermal management during
CMP at high kinematic conditions.
Aside from the apparent rise shown at the highest p × V condition, the rises in
temperature at all other p × V values were negligible despite the slurry flow rate. This
indicates that changes in slurry flow rate do not appear to significantly promote or hinder
heat generation during polishing at lower p × V conditions. This is likely due to the fact
that there was no slurry starvation effects occurring at the polishing interface under these
p × V conditions.
Figure 4.79: Mean IR temperature readings for 1.39-mm thick Freudenberg flat pad at polishing flow rates of 40 and 120 cc/min
229
Figure 4.80: Mean IR temperature plot for 1.39-mm thick Freudenberg XY-groove pad at polishing flow rates of 40 and 120 cc/min
Figure 4.81: Mean IR temperature plot for 1.39-mm thick Freudenberg perforated pad at polishing flow rates of 40 and 120 cc/min
230
If one considers a single groove type, it is apparent that the rise in temperature, or ∆T,
increases with increasing p × V. This rise in observed pad temperature can be directly
related to the increase in frictional contact at the pad-wafer interface as the pressure and
velocity parameters are increased. Based on results shown later in Chapter 5.3, it can be
shown the COF during CMP increases as the process temperature increases. This
relationship thereby indicates that there is a more vigorous contact mechanism at the
polishing interface, which can directly translate into greater heat generation. This circular
effect between increasing heat and friction can be considered perpetual until other
limiting factors such as heat absorption by slurry, or chemical limitations, create a
threshold for the generation of heat.
Since it has been established that the results in Figs. 4.79 through 4.81 show
negligible variation with respect to slurry flow rate (with the exception at 39 kPa-m/s)
and similar trends with respect to p × V, one can now focus on the variations in ∆T with
respect to variable pad grooving. The average ∆T from the lowest p × V (4 kPa-m/s) to
the highest p × V (39 kPA-m/s) was 9.0 ± 0.9, 7.6 ± 0.9 and 4.6 ± 0.6°C for the
perforated, flat and XY-groove pads respectively. Based on these results, the mechanical
impact on the heat generation was least for the XY-groove pad and greatest for the
perforated pad.
The observed variations in temperature rise for each of these pads may be a result of
two effects. The first is the impact of the ‘up-area’ of each pad groove type. The ‘up-area’
of a polishing pad, α, is the area fraction of the pad that is not grooved. Based on this
definition a flat pad would have an α value of unity (α = 1). The α values for the flat,
231
perforated and XY-groove pads used in this study were 1.0, 0.94 and 0.72 respectively.
This indicates that a greater extent of pad area is exposed to the wafer during CMP with
flat and perforated pads. Using this fact, one can argue that greater heat will be
mechanically generated with these pads as a result of the increased potential for direct
pad-wafer contact incidences.
The second aspect that could effect the mechanical contribution to temperature rise is
the impact of pad grooving on the flow and transfer of slurry during CMP. Since the XY-
groove pad has direct channels to the edge of the pad this enables slurry to eject from the
pad in an easier fashion. Since the XY-groove pad can facilitate this slurry channeling
effect, freshly dispensed slurry has a much greater ability to replace existing slurry and
interact during the polish. This efficient slurry replacement cycle has a two fold effect:
1. The slurry, which can be treated as water, has a thermal conductivity value of
approximately 0.06 W/m-K. Coupling this with the heat capacities of the
slurry and polishing pad (Cp-slurry ~ 4.184 J/g-K, Cp-pad ~ 1.456 J/g-K), one can
see that the slurry can absorb heat at a greater rate. The ability of slurry to
effectively capture heat generated during polishing, indicates that heat transfer
via the slurry properties and pad grooving can successfully lower temperatures
at the polishing interface (as seen in Figs. 4.79-4.81).
2. Effective slurry replacement and transfer can promote the rate of material
removal. This result can be seen in Chapter 4.3.2.
232
4.3.4.2 2.03-mm Pad Thickness
Figures 4.82 through 4.84 show the mean IR temperature readings for all three pad
groove types for a pad thickness of 2.03-mm and flow rates of 40 and 120 cc/min. The
observed thermal readings are plotted per polish at each individual pressure and velocity
condition. If one focuses on a single pad and observes the variations in temperature rise
for each slurry flow rate condition (40 and 120 cc/min), it can be inferred that the rises in
temperature are slightly higher for 40 cc/min at a p × V value of 39 kPa-m/s. This result
is identical to those shown for the 1.39-mm pad thickness results in Figs. 4.79-4.81. The
mean difference in temperature rise between the two flow rates at 39 kPa-m/s is
approximately 3°C. As in the 1.39-mm pad thickness results, one can associate this slight
rise in temperature to the amount of slurry on the pad at the high sliding velocity
associated with the 39 kPa-m/s condition (120 RPM). The explanation for this is
described in the prior section. As compared with the results shown in Figs. 4.79-4.81, the
average thermal rise at the 39 kPa-m/s condition is slightly greater for the thicker pads
(2.03-mm). This discrepancy in temperature rise between the two pad thicknesses is
considered to be result of variations during experimentation and can not truly be
associated any specific mechanical or chemical mechanism during CMP. Despite this, the
consistency in thermal variation with respect to slurry flow rate validates the role which
slurry plays in the thermal management during CMP at high kinematic conditions.
In addition to the similarity seen between the 1.39 and 2.03 mm pads at the highest p
× V condition, the 2.03 mm pads also showed similar increasing trends in temperature
233
rise at all other p × V values. For an individual pad grooving, the observed rising trend in
temperature with p × V was negligible with respect to slurry flow rate. Again, it is
apparent that changes in slurry flow rate do not appear to significantly promote or hinder
heat generation during polishing at lower p × V conditions.
Focusing on the variations in ∆T with respect to variable pad grooving, Figs. 4.82
through 4.84 indicate that the flat pad has the greatest rise in temperature with p × V. The
average ∆T from the lowest p × V (4 kPa-m/s) to the highest p × V (39 kPA-m/s) was 7.9
± 1.3, 11.9 ± 2.0 and 6.2 ± 1.8°C for the perforated, flat and XY-groove pads
respectively. These results appear very similar with regards to groove type as those
shown in Figs. 4.79-4.81 for the 1.39-mm pads. Based on the corresponding relationship
between the groove types for both pad thicknesses, similar practical arguments can be
used to describe the thermal phenomena.
On a further note, it can be said that pad thickness does have a contributing impact on
thermal rises during CMP. In the results for all pad groove types, the progressive rise in
temperature is always greater for the 2.03-mm pads than for the 1.39-mm pads. The rises
in temperature ranged from approximately 0.8 – 4.8°C at the lowest p ×V condition, to
0.3 – 7.9°C at the highest p × V.
234
Figure 4.82: Mean IR temperature plots for 2.03-mm thick Freudenberg flat pad at polishing flow rates of 40 and 120 cc/min
Figure 4.83: Mean IR temperature plots for 2.03-mm thick Freudenberg XY-groove pad at polishing flow rates of 40 and 120 cc/min
235
Figure 4.84: Mean IR temperature plots for 2.03-mm thick Freudenberg perforated pad at polishing flow rates of 40 and 120 cc/min
236
4.3.5 Concluding Remarks
The Freudenberg pad study was developed to provide a complete understanding and
characterization of ILD CMP with respect to changes in pad grooving, pad thickness,
platen set point temperature, slurry flow rate and kinematic process conditions. The
impact of these parameters was investigated with respect to variations in material
removal rate, changes in pad temperature as a function of changing p × V, changes in
mean COF as a function of pad temperature and the tribological mechanisms occurring
during each condition.
Material removal rate results showed that despite the pad groove type or pad
thickness, removal rates appeared linearly dependent with each set of sliding velocities
used during testing. This phenomena will be described in more detail in the following
chapter. Removal rate results, as well as regression analysis, also showed that slurry flow
rate did not appear to have a significant impact on material removal for all pad types.
Regression analysis also showed that removal rate was significantly impacted by p × V
followed by pad groove type. Finally, the removal rate results for the XY-groove pad
showed some dependence with pad thickness. Based on the results, the 1.39-mm pad
removed nearly 1000 Å/min more ILD than the 2.03-mm thickness pad. It is believed that
this effect is due to the increased rigidity of the thinner pad as well as its ability to
circulate slurry within the pad-wafer interface in a more efficient manner.
When focusing on pad temperature rises as a function of various kinematic conditions
and slurry flow rates appeared to have no significant impact on pad heating. The XY-
237
groove pad showed the lowest rise in pad temperature as compared to the flat and
perforated pads. This is believed to be a result of the pads ability to cool the pad-wafer
interface via enhanced slurry transport. One source of pad temperature rise dependence
lied in pad thickness. Based on the results shown, an increase in pad thickness appeared
to raise the apparent rise in pad temperature anywhere from 0.3–7.9°C. This observation
was true of all pad groove types.
Finally, Stibeck-Gumbel curves for all polishing conditions showed that regardless of
pad groove type, pad thickness, pad temperature or slurry flow rate, all of the tribological
mechanisms occurred within the boundary lubrication regime. As mentioned earlier,
operating in boundary lubrication allows for easier process control since there is very
little COF variation with respect to the So. The major drawback that should be considered
for these pads and future pad designs is the potential for excessive pad wear due to direct
body contact between the wafer and pad. Future studies should attempt to characterize the
rate of wear with respect to each of these pads and investigate other pad groove types as
well as alternate pad materials to minimize these pad wear effects.
238
CHAPTER 5 – ROLE OF TEMPERATURE DURING CMP
5.1 Motivation
Temperature has often been a neglected aspect of CMP and has been shown to affect
the CMP process. Since CMP is a process that involves a combination of chemical and
mechanical effects, changes in the process temperature can impact these individual
aspects a number of ways. Rises in temperature, either deliberate or via frictional contact,
can enhance chemical reaction rates at the pad-slurry-wafer interface. Furthermore, rises
in temperature can change the bulk polymeric properties of a polishing pad, thereby
either increasing or reducing removal effects. Drops in temperature create a chemically
limited CMP environment. Temperature drops also cause pad hardening, which enhance
the mechanical ability for material removal during CMP.
Thermal rises in CMP often occur as a result of frictional heating at the pad-wafer
interface or heating which is added from an outside source (heat exchangers, etc.)
Cooling during CMP can occur as a result of heat adsorption from the distribution of
fresh slurry during polishing or an external chilling source. Another form of cooling
occurs as a result of a fanning effect of the polishing pad at especially high velocity
polishes (i.e., the pad velocity is so great that heat generated at the pad surface dissipates
to the air via convection).
Heating or cooling is often applied to the platen, wafer or slurry during CMP in order
to achieve certain objectives. Industrially, it is common to find certain CMP process
239
modules in which polishing platens are cooled to below room temperature
(approximately 10°C) in order to generate stable removal rate results and sustain an
acceptable level of WIWNU (Choi, 2001). Furthermore, thermally enhanced CMP could
aid in prolonging consumable lifetimes or providing more efficient use of the
consumables.
Based on these impacts, understanding the role of temperature in CMP has become
one of the central focuses in this research. Characterizing a CMP process using variable
process temperatures leads to better comprehension of the kinetics involved in material
removal.
A bulk of this work has been done to characterize ILD films during CMP, but
subsequent sections of this dissertation will show several results from copper, as well as
tungsten CMP. Although metal CMP is not the primary focus of this research, the
emergence of metals for IC fabrication, such as copper, has drawn a significant amount of
attention to their’ processes. Furthermore, the metal CMP tests proved essential when
attempting to explain thermal effects during CMP and drawing comparisons with ILD
CMP effects.
240
5.2 Arrhenius Characterization of ILD and Copper CMP Processes
5.2.1 Background
In recent years, temperature related studies in CMP have been directed towards
understanding the effects on ILD and metal planarization (commonly tungsten). Although
temperature effects are not suspected to impact the ILD planarization process
dramatically, attempts have been made to understand silicon and ILD removal rates at
various polishing temperatures (Kim, et al., 2002; Sorooshian et al., 2003; Karaki et al.,
1978). These studies have been able to show that increases in polishing temperature are
directly proportional to ILD removal rate, but as a combination of several factors,
including the effect of temperature on pad properties, slurry chemistry (i.e., pH) and
wafer-pad contact area.
Thermal characterization of copper polishing has been evaluated with more interest
due to the greater impact of temperature on removal rate and slurry chemistry. Studies
have shown that increasing polishing temperature significantly increases copper removal
(more so than the thermal impacts on ILD) as well as dishing and erosion (Sorooshian et
al., 2003; Karaki et al., 1978; Chiou et al., 1999; Wijekoon et al., 1999; Sasaki et al.,
1998). Thermal CMP characterization has also been investigated from a modeling
perspective. To date, studies have characterized the effects of heat transfer on transient
temperature rises during polishing and the overall steady-state polishing temperatures as
241
a function of polishing pressures and velocities (White et al., 2003; Hocheng et al., 1999;
Bulsara et al., 1997).
In this study, experimental data involving the effect of polishing temperature on ILD
and copper removal rates is analyzed and fit to a newly defined Preston’s equation, which
considers the thermal contributions to material removal through an Arrhenius expression
(Preston, 1927). With a modification and redefinition of the traditional activation energy
term in the Arrhenius equation, this study presents a new parameter, the combined
activation energy, which will serve as a fundamental characterization parameter
describing the thermal dependence of CMP for various consumable sets used.
5.2.2 Theory
The development of a comprehensive CMP material removal model requires detailed
understanding of two main facets of the process. As the name suggests, CMP is a
combination of mechanical and chemical processes. The former is predominantly
governed by factors such as applied wafer pressure, sliding velocity, as well as various
mechanical attributes of the wafer, slurry, pad, and the conditioner as they relate to the
extent of normal and shear forces and stick-slip phenomena present in the pad-wafer
region. Chemical processes are mostly governed by reaction and dissolution rates in the
pad-wafer region, which in turn are driven by solution pH, ionic strength and the
chemical nature of various additives and abrasives in the slurry. The chemical make-up of
242
the wafer and pad also play critical roles in establishing the extent of material removal
during CMP.
As described in Chapter 1, removal rate in CMP has been traditionally characterized
using the Preston’s equation shown by Eqn.. (1.7). A more general form of the Preston’s
equation is shown in Eqn.. (5.1) and is used as the basis for the model in this work.
omn RRVpkRR +⋅⋅= (5.1)
In Eqn. (5.1), RR is the material removal rate, k is the Preston’s constant, p is the
applied wafer pressure, V is the pad-wafer sliding velocity, and RRo represents the
dynamic etch rate of the wafer material in the absence of pressure and velocity. The latter
term has been shown to be insignificant for ILD applications, but critical for polishing of
copper and tungsten (Chiou et al., 1999). The exponential parameters n and m are fitted
values that vary based on the consumable set being used. The above equation is grossly
generalized since it relies on essentially one constant, k, to capture and represent all other
chemical and mechanical intricacies of the process.
During CMP, polishing temperatures can rise due to friction, chemical reaction and
dissolution (Kim et al., 2002; White et al., 2003; Bulsara et al., 1997). If sufficient, the
rise in temperature can impact the chemical attributes of material removal (through an
Arrhenius relationship), as well as the mechanical aspects of the process (through a
change in thermo-elastic properties of the pad) (Chiou et al., 1999; Olsen, 2002). This
study introduces a new definition of the Preston’s constant, k, which considers the effect
of polishing temperatures through an Arrhenius relationship and a newly defined
‘thermally independent constant’, κ. In Eqn. (5.2), Ecomb denotes the combined activation
243
energy of the process, which is not considered to be solely chemical in the traditional
definition of activation energy. By definition, the new combined activation energy term
describes all events, chemical or mechanical, that are impacted by temperature during the
CMP process. Additionally, R and T represent the gas constant and the temperature of the
process, respectively.
−
⋅=RTEk combexpκ (5.2)
Incorporation of the above definition into Eqn. (5.1) can be further manipulated to
generate a linear relationship between the effective removal rate and the inverse of
temperature. In this study, effective removal rate (RRe) is defined as the component of the
total removal rate at non-zero applied wafer pressures and pad-wafer sliding velocities in
accordance with Eqn. (5.3) below:
oe RRRRRR −= . (5.3)
Through a logarithmic rearrangement, Preston’s equation becomes:
)ln()ln()ln( mncombe UP
RTERR ⋅+
−= κ (5.4)
By plotting the natural log of the effective removal rate against the inverse of
temperature, an Arrhenius relationship for the process can be observed.
244
5.2.3 Experimental Approach
The CMP experiments performed for this study were done at the IPL and
incorporated the use of the scaled polisher described in Chapter 2.1. Platen temperatures
for this study were controlled using the technique described in Chapter 2.1.9. Desired
platen set point temperatures of 17, 25, 35 and 45ºC were used for the polishes of this
study. Prior to polishing the desired pad temperature was kept at steady state for 5
minutes.
The IR camera described in Chapter 2.3.2 was used to monitor the pad surface
temperature prior to and during polishing. As described in that section, the mean process
temperature of a polish was calculated as the average value of the ten temperature points
shown in Fig. 2.23.
All polishes were performed at wafer pressures ranging from 2 to 6 PSI and sliding
velocities ranging from 0.31 to 0.93 m/s. Polishes were repeated at least twice per
condition. Across the range of pressures and velocities noted above, for a given isotherm,
the total fluctuation in temperature was no more than 4ºC.
ILD Polishing: ILD polishes were performed for one minute on 100-mm blanket
silicon wafers with 500-nm of thermally grown silicon dioxide. Two different pads
(without any sub-pads) were employed for the experiments: Rohm and Haas’s IC-1000 k-
groove pad and JSR’s WSP soft non-porous pad. Fujimi PL-4217 slurry was paired with
the Rohm and Haas pad while JSR’s CMS1101 slurry was used when polishing with the
WSP pad. The slurries used in conjunction with the above pads were quite similar to one
245
another in terms of the type of abrasive (i.e., fumed silica), the slurry pH (approximately
10.8), the type of base (KOH), abrasive content (approximately 12.5 percent by weight),
and mean aggregate size (approximately 110-nm). In all cases, slurry flow rate was kept
constant at 80 cc/min.
Prior to ILD polishing, the pad was conditioned for 30-minutes using slurry. In the
case of IC-1000 pads, conditioning consisted of a perforated 100-grit diamond disc
conditioner. For the WSP pad, conditioning was performed using a ring-type 325-grit
diamond disc conditioner. Conditioning parameters for both pad types involved a
pressure of 3.5 kPa (0.5 PSI), rotational velocity of 20 RPM and disk sweep frequency of
30 per minute. Conditioning was followed by a 5-minute pad break-in with a dummy
wafer. On a final note, ILD experiments using the IC-1000 pad were performed in-situ,
whereas tests using the WSP pad were performed ex-situ with conditioning intervals of
one minute. After polishing, all wafers were rinsed, dried and measured for oxide
thickness using a 40 point scan on a Filmetrics F20 tool.
Copper Polishing: Copper polishes were performed for two minutes on 100-mm
copper metal discs with a purity of 99.95 percent. Rohm and Haas’s IC-1000 XY-groove
pad (without a sub-pad) was used in conjunction with Fujimi’s PL-7102 slurry containing
hydrogen peroxide as the oxidizer (pH~6.8). All polishes were run at a flow rate of 155
cc/min. The pad was conditioned with ultra-pure water using identical conditions as those
described for ILD polishing with an IC-1000 pad and followed by a 5-minute pad break-
in with a dummy wafer. Following polishing, all discs were rinsed, dried and measured
for mass loss using the Ohaus analytical scale described in Chapter 2.3.3.
246
5.2.3 Results and Discussion
ILD Polishing – Figure 5.1 shows the Arrhenius relationship associated with ILD
polishing using Rohm and Haas and JSR pads. As expected, the resulting material
removal rate data for various values of p × V result in linear relationships with the inverse
of temperature. The slopes associated with each p × V setting are near equivalent to one
another. This analysis indicates that in spite of differences in polishing conditions (i.e.,
different values of pressures and velocities) the effect of temperature on material removal
impacts all p × V conditions in a similar and relative manner (i.e., all lines in Fig. 5.1 are
parallel).
Using Eqn. (5.4) in conjunction with the slopes obtained from Fig. 5.2, the combined
activation energy for each process condition can be calculated. The Arrhenius
relationship associated with ILD polishing with Rohm and Haas and JSR pads
consistently resulted in average combined activation energies of 0.06 ± 0.04 and 0.07 ±
0.04 eV, respectively. As mentioned before, the dynamic etch rate of silicon dioxide is
zero (i.e., RRo equals zero, and the best line fit between ILD removal rate and p × V goes
through the origin). Due to this, one can assume that the predominant phenomenon
responsible for oxide removal is a combination of chemical and mechanical interactions
as they relate to the hydration of the oxide surface in the presence of the alkaline slurry
followed by mechanical abrasion by the pad and abrasive particles. As described in
Chapter 1.4.2, it could be postulated that the chemical contribution to the combined
247
activation energies calculated above, represent the reaction between the siloxane bonds
and water (Eqn. (1.2)) as they occur in CMP (Cook, 1990).
By manipulating Eqn. (5.2), the equation below can be used to evaluate the relative
contributions of the thermally dependent and thermally independent factors in each
system.
RTEk comb−= )ln()ln( κ . (5.5)
Based on Eqn. (5.5), the ILD polish process with the Rohm and Haas pad shows an
average thermally dependent contribution to the Preston’s constant of approximately 8
percent.
Figure 5.1: Arrhenius relationship for 1-minute ILD polish on Rohm and Haas IC-1000 k-groove pad (a) and JSR WSP pad (b). Note that units of m/s were used for the RR term on the y-axis
(a)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
R)
p x U = 5.15E03 (Pa m/s)
p x U = 1.55E04 (Pa m/s)
p x U = 4.64E04 (Pa m/s)
(b)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
R)
p x U = 5.15E03 (Pa m/s)
p x U = 1.03E04 (Pa m/s)
p x U = 3.09E04 (Pa m/s)
(a)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
R)
p x U = 5.15E03 (Pa m/s)
p x U = 1.55E04 (Pa m/s)
p x U = 4.64E04 (Pa m/s)
(a)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
R)
p x U = 5.15E03 (Pa m/s)
p x U = 1.55E04 (Pa m/s)
p x U = 4.64E04 (Pa m/s)
(b)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
R)
p x U = 5.15E03 (Pa m/s)
p x U = 1.03E04 (Pa m/s)
p x U = 3.09E04 (Pa m/s)
(b)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
R)
p x U = 5.15E03 (Pa m/s)
p x U = 1.03E04 (Pa m/s)
p x U = 3.09E04 (Pa m/s)
248
Similarly, the average thermally dependent contribution associated with the process
using the JSR pad is calculated to be about 9 percent. This slight increase is possibly
caused by the enhanced chemical properties of the JSR pad due to the dependence of the
solubility of water-soluble particles on temperature. This hypothesis is currently under
detailed investigation.
Copper Polishing – Figure 5.2 shows the Arrhenius relationship corresponding to
various values of p5/6 × V1/2 (i.e., for each respective process condition) at a slurry flow
rate of 155 cc/min. Note that the exponential values of 5/6 and 1/2 on the pressure and
velocity terms, respectively, are associated with the Tseng and Wang model of the
Preston’s equation. The Tseng and Wang model was used in conjunction with these data
due to the inherent nature of non-linear removal rates associated with copper polishing
(Tseng et al., 1997).
In order to overcome potential reactant depletion problems (i.e., slurry starvation),
removal rate experiments were done using a relatively high slurry flow rate of 155 cc/min
at various pad temperatures. As seen from Fig. 5.2, the average combined activation
energy for a copper polishing process was calculated to be 0.52 ± 0.06 eV. As in the case
of ILD, a hypothetical surface reaction for copper removal can be associated to the above
combined activation energy. Although the mechanism for copper removal has not yet
been fully developed, one could hypothesize that copper removal with a peroxide based
slurry could occur as a sequence of Eqns. (5.6) and (5.7) (Lu, et al., 2003).
OHOCuOHCu 222222 +↔+ (5.6)
OHCuOOHOCu 2222 2 +↔+ (5.7)
249
As mentioned before, RRo plays a critical role in copper CMP due to the information
it provides about the true chemical contribution to the polishing process. Unlike the ILD
process in which temperature impacts polishing through the combined effect of chemical
and mechanical interactions (i.e., RRo equals zero), the role of temperature in copper
CMP can be used to independently determine the relative contributions during pure
chemical interactions as well as the combined chemical and mechanical interactions. This
concept can be explained by comparing the values contained in the exponential terms of
Eqn. (5.8), the Arrhenius rate equation describing dynamic etch rates, and Eqn. (5.2). In
Eqn. (5.8), k’ is a product of the Arrhenius pre-exponential constant and an undetermined
characteristic length, which provides the dynamic etch rate units of length per time.
Furthermore, Ea is the chemical activation energy for the copper removal mechanism
during CMP.
)exp(*
RTEkRR a
o−
⋅= (5.8)
Based on the previous assumption that the combined activation energy is a parameter
involving both the chemical and mechanical events in CMP impacted by temperature, it
is hypothesized that the chemical activation energy observed in Eqn. (5.8) is also a
contributing factor to the Ecomb parameter. As a result of this hypothesis, a relative
comparison between the combined activation energy and the chemical activation energy
can potentially provide some insight as to which facet of CMP, chemical or mechanical,
is dominant during polishing.
As seen in Fig. 5.3(a), an extrapolation of typical removal rate and p × V data and the
determination of the y-intercept allows one to roughly determine the value of RRo without
250
resorting to performing actual dynamic copper etch rate studies in a beaker. As a result,
this extrapolation represents only the true chemical removal of copper in the absence of
any mechanical effects. Through a series of controlled temperature runs, values of RRo
(extrapolated based on the above technique) can be plotted as a function of the inverse of
temperature to provide yet another Arrhenius relationship, which now represents the
theoretical chemical activation energy of the system, Ea. Figure 5.3(b) indicates that the
true theoretical chemical activation energy of the copper system is 0.36 ± 0.19 eV.
Figure 5.2: Arrhenius relationship for a 1-minute copper polish on IC-1000 XY-groove pad at a flow rate of 155 cc/min
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
Re)
p x U = 1.03E04 (Pa m/s)
p x U = 3.09E04 (Pa m/s)
251
From the aforementioned hypothesis, a simple calculation can be made to determine
the relative contribution of the chemical effects of the process (i.e., Ea) to the combined
activation energy. It is estimated that the true chemical contribution to the combined
activation energy is nearly 69 percent, thus indicating that copper polishing is greatly
impacted by chemical effects alone. From a qualitative point of view, this finding is not
surprising, however the fact that Arrhenius-type analysis can quantify the extent of the
chemical effects is remarkable. It is envisaged that analysis of this nature can help design
improved slurries for metal CMP applications.
Figure 5.3: (a) Removal rate data for a 1-minute copper polish at 25°C, indicating the extrapolated dynamic etch rate across the y-axis. (b) Arrhenius relationship for the theoretically pure chemical activation energy using various dynamic etch rates at various pad temperatures. Note that units of m/s were used for the RR term on the y-axis
(a) (b)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
Ro)
P x u = 0
y = 1.35E-12x + 9.43E-10R2 = 9.88E-01
0.E+00
2.E-09
4.E-09
6.E-09
8.E-09
1.E-08
0 2500 5000 7500 10000
P5/6 x u1/2 (Pa m/s)
Rem
oval
Rat
e (m
/s)
RRo ~ 550 Å / min
p5/6 × V1/2 (Pa-m/s)
(a) (b)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
Ro)
P x u = 0
(b)
-23.0
-22.0
-21.0
-20.0
-19.0
-18.0
0.0031 0.0032 0.0033 0.0034 0.0035
1/T (K-1)
ln (R
Ro)
P x u = 0
y = 1.35E-12x + 9.43E-10R2 = 9.88E-01
0.E+00
2.E-09
4.E-09
6.E-09
8.E-09
1.E-08
0 2500 5000 7500 10000
P5/6 x u1/2 (Pa m/s)
Rem
oval
Rat
e (m
/s)
RRo ~ 550 Å / min
p5/6 × V1/2 (Pa-m/s)
y = 1.35E-12x + 9.43E-10R2 = 9.88E-01
0.E+00
2.E-09
4.E-09
6.E-09
8.E-09
1.E-08
0 2500 5000 7500 10000
P5/6 x u1/2 (Pa m/s)
Rem
oval
Rat
e (m
/s)
RRo ~ 550 Å / min
p5/6 × V1/2 (Pa-m/s)
252
Referring to the general concept of thermally dependent and thermally independent
contributions to copper CMP, similar analysis can be performed by applying Eqn. (5.5).
Results indicate that the average thermally dependent contribution associated with the
copper process is 62 percent (based on the more accurate high flow rate data sets).
Compared to the ILD CMP results, the thermal contribution to the copper process is
approximately nine times greater. This sharp difference is justified through previous
discussions where purely chemical effects were shown to account for roughly 69 percent
of the entire material removal phenomena.
5.2.4 Concluding Remarks
By modifying the generalized Preston’s equation to employ an Arrhenius argument,
this study introduced a new parameter described as the combined activation energy.
Based on this new parameter, the impacts of pad temperature on the chemical and
mechanical facets of CMP were capable of being quantified into a single defined value,
which showed the differences between various dependencies arising from the use of
different of consumable sets. For ILD polishing, results indicated that the Rohm and Haas
IC-1000 pad with Fujimi PL-4217 slurry resulted in a combined activation energy of 0.06
eV. This was slightly lower than the 0.07 eV generated by the JSR pad and slurry.
Copper polishing resulted in a combined activation energy of 0.52 eV, which indicates a
more thermally dependent process.
253
Furthermore, results indicated that information regarding the relative magnitude of
the thermally dependent and thermally independent aspects of the ILD and copper CMP
processes (as triggered by controlled thermal changes in the system) can be critical in
designing novel pads and slurries with controlled chemical and mechanical attributes.
5.3 Effect of Process Temperature on Coefficient of Friction During CMP
5.3.1 Background
Recent publications have provided fundamental insight concerning the role of process
temperature on material removal rate during the CMP of ILD and copper films
(Philipossian et al., 2003; Cornely, 2003; Kim et al., 2002; Sorooshian et al., 2004;
Hocheng et al., 1999; White et al., 2003). These in turn have led to the development of
thermal models describing the generation of heat as a result of frictional effects caused by
shaft work at the pad-slurry-wafer interface (White et al., 2003; Li et al., 2003). In these
cases, given that thermal effects are small in magnitude (i.e., up to 8° C) and transient in
nature (i.e., temperature rises during the first 30 seconds of a 75-second polishing
process, and remains constant thereafter), it is critical to determine how sustained thermal
inputs (i.e., in the form of external platen heating or cooling) affect the frictional
characteristics of ILD and copper CMP processes (Borucki et al., 2003). Information of
this nature is critical for establishing pad life and designing pads with stable dynamic
254
mechanical properties (Olsen, 2002). Furthermore, for ILD CMP, it has been shown that
removal rate (i.e., as represented by Preston’s constant, k) and average COF are linearly
related at slurry abrasive concentrations of 9 percent or larger for a variety of pad types
(Olsen, 2002).
This work has been based on the premise that during planarization, temperature
increases in the pad-slurry-wafer region cause the dynamic mechanical properties of
CMP pads to change, thus changing the COF. Such phenomena require a fundamental
understanding of the magnitude of forces involved in the process in order to refine
existing removal rate and lubrication models.
5.3.2 Experimental Approach
The CMP experiments performed for this study were done at the IPL and
incorporated the use of the scaled polisher described in Chapter 2.1. The acquisition of
COF data for this study have been described in Chapter 2.1.6. Platen temperatures for this
study were controlled using the technique described in Chapter 2.1.9. Desired platen set
point temperatures of 12, 22, 35 and 45ºC were used for the polishes of this study. Prior
to polishing the desired pad temperature was kept at steady state for 5 minutes.
The IR camera described in Chapter 2.3.2 was used to record the pad surface
temperature prior to and during polishing. As described in that section, the mean process
temperature of a polish was calculated as the average value of the ten temperature points
shown in Fig. 2.23.
255
Polishes were performed at wafer pressures ranging from 2 to 6 PSI and a sliding
velocity of 0.31 m/s. Over the range of pressures and velocities noted above, for a given
isotherm, the total fluctuation in temperature was no more than 3°C. In the case of ILD
experiments, polishes were performed for 90 seconds on 100-mm blanket silicon wafers
having 500 nm of thermally grown silicon dioxide. Rohm and Haas’s IC-1000 K-groove
porous polyurethane pad (without a sub-pad) in conjunction with Fujimi’s PL-4217 slurry
were employed for the tests (pH~11). Slurry flow rate was kept constant at 155 ml/min in
order to avoid any mass transfer issues. For copper CMP experiments, polishes were
performed for 120 seconds on 100-mm copper discs with a purity of 99.95 percent. Rohm
and Haas’s IC-1000 XY-groove pad (without a sub-pad) was used in conjunction with
Fujimi’s PL-7102 slurry containing hydrogen peroxide as the oxidizer (pH~6.8). Slurry
flow rate was maintained at 155 ml/min. Prior to ILD polishing, the pad was conditioned
for 30-minutes using 12.5 percent by weight fumed silica slurry. For copper polishing,
ultra-pure water was used to condition the pad. In both cases, conditioning consisted of a
100-grit diamond disc (perforated design) at a pressure of 3.5 kPa (0.5 PSI), rotational
velocity of 20 RPM and disk sweep frequency of 30 per minute. Conditioning was
followed by a 5-minute pad break-in with a dummy wafer.
DMA analysis of the polishing pads used in this study were completed using the
described method from Chapter 2.3.1.1.
256
5.3.3 Results and Discussion
Figure 5.4 shows the effect of process temperature on COF for both ILD and copper
CMP processes. Increasing platen temperature increases COF for ILD and copper
processes. Each data point in Fig. 5.4 represents an average of eight polishes at various
pressures and velocities. In all cases, standard deviation was less than ± 5 percent. This
trend is believed to be due to the effect of higher temperatures on the mechanical
properties of the pad.
Figure 5.4: Dependence of COF as a function of average pad temperature for 90-second ILD and copper polishes at multiple wafer pressures and pad-wafer velocities
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40 50
Average Pad Temperature (°C)
Coe
ffici
ent o
f Fric
tion
ILD
Copper
257
Figures 5.5 and 5.6 present DMA results for both the flexural storage modulus and
tan δ of both pad types. As described in Chapter 2.3.1.1, flexural storage modulus is a
parameter used to describe the bulk softening of the pad while tan δ is a measure of the
toughness of the material. In Fig. 5.5, the flexural storage moduli of both the K-groove
and the XY-groove pads used in ILD and copper polishing decrease as a function of
temperature. In the case of the k-groove pad, the flexural storage modulus decreases from
377 to 218 MPa (approximately 42 percent) over the range of temperatures set during
polishing (all results were obtained at 10 Hz). For the XY-groove pad, the decrease
occurs from 667 to 491 MPa (approximately 26 percent). Since these percentages
correspond to the softening of the pad, for a constant normal force, a softer pad will
experience a greater shear force at the leading edge of the wafer during polish.
The reason for this is two-fold. First, on a macro-scale the softer pad will become
further compressed at the leading edge of the wafer in response to the applied normal
load. This compression will subsequently result in the formation of a barrier, which the
wafer has to overcome continuously during its motion on the surface of the pad. Second,
on a micro-scale, the pad asperities in the wafer-pad region will tend to collapse due to
the relative softness of the pad. These two phenomena combine to increase the net shear
force between the wafer and the pad and hence the COF for the softer pad as compared to
the harder pad.
In Fig. 5.4, the observation that COF is more sensitive to temperature for copper
polish cannot yet be explained due to the presence of several confounding factors: (1)
ILD polishing was done with a K-groove pad, while copper polishing was performed
258
with a XY-groove pad. Based on the differences in groove type, slurry transport between
the pad and wafer may have affected COF. (2) Different slurries (i.e., different
chemistries, additives, abrasive types and abrasive concentrations) were used for copper
and ILD experiments. Since the hypothetical mechanisms for ILD and copper removal
vary with respect to the specific slurry chemistries used, temperature could play a
significant role in affecting shear force. For example, in the case of copper CMP
processes, the formation and subsequent removal of a copper oxide layer has been shown
to be impacted by changes in pad temperature to a much greater extent than with ILD
(Sorooshian et al., 2004). For example, one possibility would be that at higher
temperatures, the oxide that grows on the Cu is thicker or potentially rougher. This effect
is very likely to happen at high temperatures and increase COF.
An additional factor that may be contributing to the increase in COF as a function of
process temperature is the increasing trend in tan δ as a function of temperature (Fig.
5.6). For a polymeric material sliding on a rigid body, tan δ, which is the ratio of flexural
storage modulus and loss modulus, is shown to be directly proportional to shear force
(Fs) as shown in the equation below (Moore, 1975)
δσ tan
∝
HWFs . (5.9)
In Eqn. (5.9) W is the applied load for the process, σ is the maximum stress on a given
area and H is the hardness of the polymer. By qualitatively applying the above
relationship to CMP, as a first order approximation for a given load and process
temperature, one can assume the ratio of stress to material hardness to be constant.
259
Figure 5.5: Flexural storage modulus results for as-received IC-1000 K-groove and XY-groove pads. Tests were performed over the range of temperatures observed during polishing experiments
Figure 5.6: Tan δ results for as-received IC-1000 K-groove and XY-groove pads. Tests were performed over the range of temperatures observed during polishing experiments
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50Pad Temperature (°C)
Flex
ular
Sto
rage
Mod
ulus
(MPa
) K-grooveXY-groove
0.05
0.06
0.07
0.08
0.09
0.1
0 10 20 30 40 50Pad Temperature (°C)
Tan δ
K-grooveXY-groove
260
By these approximations the increase in COF can in part be explained by a 25 and 14
percent increases in tan δ for the ILD and copper CMP processes, respectively.
5.3.4 Concluding Remarks
Based on a series of controlled temperature polishes, COF results indicate that a rise
in polishing temperature creates a rise in shear force for both ILD and copper CMP.
DMA results yielded supporting evidence towards this observation. Physical correlations
drawn between pad-wafer contact and pad softening show that rises in shear force could
result from the wafer having to overcome a formation barrier generated by the softening
of the pad surface.
Furthermore, it was shown that the rise in COF could partially be explained through a
proportionality relationship of shear force and tan δ. By assuming a constant ratio of pad
stress to pad hardness, the aforementioned relationship yields a fairly accurate first order
approximation of the observations seen from this study. As to the variations in COF rise
with temperature for ILD and copper polishing, one could attribute these dissimilarities to
variations in the consumable sets used (i.e., pad grooving and its affect on slurry
transport, slurry type and concentration), and/or the affect of temperature on the
mechanism of ILD and copper removal.
261
5.4 Revisiting the Removal Rate Model for Oxide CMP
5.4.1 Objective
The following study seeks to explain removal rate trends and scatter in thermal
silicon dioxide and PE-CVD tetraethoxysilane-sourced silicon dioxide (PE-TEOS) CMP
using an augmented version of the Langmuir-Hinshelwood mechanism. The proposed
model is an extension of the study presented in Chapter 5.2 and combines the chemical
and mechanical facets of ILD CMP and hypothesizes that the chemical reaction
temperature is determined by transient flash heating.
The removal rate models described in Chapter 1.5.4 illustrate certain observed
Prestonian and non-Prestonian trends in ILD removal rates. Stein and Hetherington
(S&H) evaluated the relative predictive capabilities of these and other models by
comparing the best fit of each model with measured blanket thermal oxide (TOX)
removal rates (Stein et al., 2002). Polishing was performed on a Speedfam-IPEC 472
polisher using Rohm and Haas IC-1400 K-groove pads and Fujimi SS-12 fumed silica
slurry. It was found that the average fitting errors using the Preston, Zhang & Busnaina,
Tseng & Wang, and Zhao & Shi models were approximately 370, 493, 271 and 440
Å/min respectively. To gauge the severity of these fitting errors, one of the experimental
conditions in S&H (6 PSI, 60 RPM) was repeated four times. Fig. 5.7 shows data from
S&H in which a mean rate of 3079 Å/min was measured at the repeated condition with a
standard deviation of 67 Å/min (approximately 2 percent 1-sigma variation). The model
262
fitting errors are thus significantly larger than the replication error. However, when the
Stein and Hetherington TOX removal rate data in Fig. 5.7 are grouped according to
sliding velocity, one can see distinct trends in the removal rate with increasing pressure.
This suggests that what at first appears to be random scatter may be systematic.
Figure 5.7: Thermal silicon dioxide removal rate data from S&H grouped by pad-wafer sliding velocities (Stein et al., 2002)
This study will explain trends and scatter in TOX and thermally annealed PECVD
PE-TEOS removal rates using an augmented version of the Langmuir-Hinshelwood
mechanism. The proposed model includes the chemical and mechanical aspects of ILD
CMP and hyothesizes that the chemical reaction temperature is dominated mainly by
0
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0 20 40 60 80 100p x V (kPa m/s)
Ther
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30 RPM
45 RPM
60 RPM
75 RPM
90 RPM
p × V (kW/m2)
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0 20 40 60 80 100p x V (kPa m/s)
Ther
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45 RPM
60 RPM
75 RPM
90 RPM
p × V (kW/m2)
263
transient flash heating. The accuracy and predictive capability of the proposed removal
rate model confirms that the data scatter described above is systematic and explainable.
To emphasize this point, we also use a method of visualizing removal rate data that
suggests, apart from any particular interpretative theory, that a smooth and easily
interpretable surface underlies the apparent scatter.
5.4.2 Experimental Approach
The CMP experiments performed for this study were done at SNL and incorporated
the use of the SpeedFam-IPEC 472 polisher described in Chapter 2.2. Platen temperatures
for this study were controlled using the technique described in Chapter 2.1.9.
The IR camera described in Chapter 2.3.2 was used to record the pad surface
temperature prior to and during polishing. As described in that section, the mean process
temperature of a polish was calculated as the average value of the ten temperature points
shown in Fig. 2.23.
Wafers used for the CMP experiments were 150-mm diameter silicon wafers with 2-
mm blanket TOX or PE-TEOS films. The polishing time per wafer was 180 sec. On the
primary platen, polishing experiments were run with in-situ conditioning at a conditioner
pressure of 0.5 PSI. Cabot D7300 fumed silica slurry (approximately 12.5 percent solid
by weight with pH~11) was used with a Rohm and Haas IC-1400 K-grooved polishing
pad. The IC-1400 K-grooved polishing pad surface is patterned with closely spaced
concentric grooves that are about 0.2 mm wide, 0.5 mm deep and approximately 1 mm
264
apart. The slurry flow rate was 270 cc/min for all runs. The following load and rotation
rate conditions were used:
• Pad-wafer sliding velocity = 0.5 m/s, Applied wafer pressure = 3 and 7 PSI
• Pad-wafer sliding velocity = 1.00 m/s, Applied wafer pressure = 6 PSI
• Pad-wafer sliding velocity = 1.51 m/s, Applied wafer pressure = 3, 5 and 7 PSI
For each film material polished, all pressure/velocity conditions were run twice in
order to assess data repeatability. All polishing conditions were also run at initial platen
set point temperatures of approximately 13, 24, 33 and 43°C. It should be noted that the
platen set point temperature does not remain constant during polishing, but provides a
desired initial thermal condition for polishing experiments. Prior to polishing, the pad
temperature was monitored until a steady state temperature was reached for at least 2
minutes. As noted above, the desired platen set point temperature is not the same as the
actual temperature that was recorded using IR during polishing. The set point temperature
creates a general variation in the thermal environment. Frictional heating induced by
polishing causes the local temperature to exceed the initial set point temperature.
On the secondary platen, used for buffing, the wafer pressure was 5 PSI and the
carrier and platen rotated at 10 and 100 RPM, respectively. The buffing step was for 30
seconds on a Fujimi Surfin SSW1 pad using ultra-pure water. Following each polish,
wafers were mechanically scrubbed using PVA brush rollers in an OnTrak DSS-200
265
scrubber. SiO2 film pre- and post thicknesses were measured using a KLA-Tencor UV-
1250 ellipsometer.
5.4.3 Experimental Results
Measured removal rates, including all replicates, are shown in Fig. 5.8 as a function
of p × V for TOX and PE-TEOS wafers polished at room temperature (platen temperature
approximately 24°C). Figure 5.8 will be referred to as a Preston plot. In Fig. 5.8(a), data
points are labeled pV1-pV6 in order of increasing p × V for further reference in this and
similar figures. From Fig. 5.8, it is apparent that PE-TEOS always polished faster than
thermal oxide. It is likely that this is due to a difference in material density. While the
rates appear to be considerably scattered, both materials show the same qualitative
variation in rate with p × V. For TOX, the RMS difference between replicates at fixed p
× V was 150 Å/min, or 8.7 percent of the mean rate at each p × V condition. For PE-
TEOS, it was 76 Å/min or 3.5 percent of the mean rate. Thus, the variation in rate at each
p × V condition was much less than the variation in rate between conditions, indicating
that the pattern of removal rate change between p × V conditions is systematic and
reproducible. At the lowest pressure, 3 PSI (pV1, pV3), the removal rate decreases with
increasing rotation rate; this difference also exceeds the replication error, thereby
indicating that both the PE-TEOS and TOX polishing data have features that are similar,
systematic and considerably non-Prestonian.
266
Figure 5.8: Room temperature removal rates for (a) thermal oxide and (b) PE-TEOS
Figure 5.9 shows an alternative method of plotting wear data originally presented by
Lim and Ashby (Lim et al., 1987; Williams, 1999). See also the use of this kind of plot
by Lefevre et al., (Lefevre et al., 2002). In this figure, contours of PE-TEOS removal rate
are plotted as a function of pressure on one axis and velocity on the other. The plot is
constructed by triangulating the individual (p,V) points and using the triangulation to
linearly interpolate the rate data. Triangle sides are shown for convenience using light
lines; individual (p,V) points lie at the corners of the triangles. Mean removal rates are
used at each point. Figure 5.9 will be referred to as a Lim-Ashby plot or wear plot. Unlike
the Preston plot, the Lim-Ashby plot shows the separate influences of p and V rather than
presupposing a dependence of rate solely on p × V. It is this presupposition that produces
the appearance of scatter in the Preston plot. For the PE-TEOS data, it is apparent that the
0
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Ther
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Oxi
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(Å/m
in)
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0 20 40 60 80pV (kW/m2)
PE
-TEO
S R
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ate
(Å/m
in)
pV13 PSI, 30 RPM
pV67 PSI, 90 RPM
pV55 PSI, 90 RPM
pV46 PSI, 60 RPM
pV33 PSI, 90 RPM
pV27 PSI, 30 RPM
TOX PE-TEOS
(a) (b)
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0 20 40 60 80pV (kW/m2)
Ther
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0 20 40 60 80pV (kW/m2)
PE
-TEO
S R
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(Å/m
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pV13 PSI, 30 RPM
pV67 PSI, 90 RPM
pV55 PSI, 90 RPM
pV46 PSI, 60 RPM
pV33 PSI, 90 RPM
pV27 PSI, 30 RPM
TOX PE-TEOS
(a) (b)
267
removal rate is pressure-dependent at all velocities and is weakly dependent on velocity
at a fixed pressure.
Figure 5.9: Lim-Ashby contour plot of the PE-TEOS removal rates in Fig. 5.8(b). The contour interval is 500 Å/min. The grey lines show a triangulation of the individual (p,V) pairs used in the experiment in Fig. 5.8(b). The triangles are used for linear interpolation of the measured rates
Figure 5.10 shows the dependence of the PE-TEOS polish rate on the platen set point
temperature. At all platen temperatures, the rate follows the same pattern of variation
with p × V as at room temperature. For all of the PE-TEOS data as a group, differences
between replicates averaged 65 Å/min or 3.0 percent in variation with exact ranges of 46-
76 Å/min and 1.1 percent to 4.4 percent variation. Thus, the pattern of variation with p ×
V is highly reproducible. At the highest p × V, the removal rate increases strongly with
platen temperature, evidence that the rate is being influenced by a thermally-activated
process. At the lowest p × V, the removal rate still has some temperature dependence but
1000 Å/min
3000 Å/min
2000 Å/min
1000 Å/min
3000 Å/min
2000 Å/min
268
the strength of the dependence is much weaker. Figure 5.11 plots the removal rate data
from Fig. 5.10 against 1/kT, where T is the mean pad temperature from IR measurements.
Figure 5.10: PE-TEOS removal rate as a function of p × V and platen temperature set point. Data were not obtained at 41 and 52 kW/m2 at a platen set point of 13°C
As described in previous sections, the mean pad temperature is the overall average of
the readings taken at all ten sample locations over the duration of a polish. Because of
frictional heating, this temperature is different from the platen set point temperature. It
can be seen from this figure that plots of the log of the removal rate vs. 1/kT imply
different activation energies at each fixed p × V. Based on this, one can call this the
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5000
0 20 40 60 80pV (kW/m2)
PE
-TE
OS
Rem
oval
Rat
e (Å
/min
) 43°C33°C24°C13°C
269
apparent activation energy and the physical significance of this parameter will be
discussed later.
All of the trends of rate with p × V and platen temperature set point were also
observed for thermal oxide. TOX polish rate data are shown in Fig. 5.12.
Figure 5.11: PE-TEOS removal rates (see Fig. 5.10) vs. the inverse of the mean pad temperature (i.e., the average recorded IR pad temperature over the entire duration of a polish) rather than the platen set point. Data are separated by p × V. Adjacent pairs of points at each p × V are replicates
270
Figure 5.12: Thermal silicon dioxide removal rate as a function of p × V and platen temperature set point. Data were not obtained at 41 and 52 kW/m2 for a platen set point of 13°C
5.4.4 Theory
The starting point for the theoretical explanation of the experimental data is a
modified Langmuir-Hinshelwood model (or flash heating model), which is explicitly
written as
pVcAepVcAeM
RRp
kTEp
kTEw
+= −
−
/
/
ρ. (5.10)
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5000
0 20 40 60 80pV (kW/m2)
Ther
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43°C33°C24°C13°C
271
This model requires knowledge of the temperature, T, at which the controlling
hydrolyzed layer formation reaction takes place. The sole extension of this model is that
for T, the functional form
pVVTT aa )/(β+= , (5.11)
where Ta is the platen set point temperature and b and a are constants. As shown in
Appendix A, the factor b/Va in Eqn. (5.11) arises from a wafer-averaged model for
asperity flash heating and from the velocity dependence of the fraction of heat that is
conducted into the pad.
Equations (5.10) and (5.11) comprise the entire model that will be used here.
Analogous to the customary practice for Preston’s equation and the models described in
the introduction, the model will be applied as a compact model in which parameters are
extracted from data. There are five independent unknown parameters: A, E, cp, and the
parameters a and b in the temperature model. It should be noted that in the absence of
knowledge of the temperature at the reaction site (as contrasted with the pad or platen
temperature), one can not, in general, expect to determine the true activation energy E of
the controlling reaction. In order to address this matter, a procedure described in is used
in which E is considered an independent variable and values of the remaining parameters
are determined as functions of E (Borucki et al., 2004). This procedure has the advantage
of providing some information about the certainty with which the other parameters can be
known. In this case, however, heated platen data also allow us to estimate E.
Following this method, Figs. 5.13, 5.14 and 5.15(a) show the least squares error and
best fitting values of A, cp, a, and b that were extracted from the room-temperature PE-
272
TEOS data in Fig. 5.8(b) using a downhill simplex optimization algorithm for E between
0.25 and 2.0 eV (Press et al., 1992). It can be seen from Fig. 5.13(a) that the least squares
fitting error is uniformly between 95 Å/min and 110 Å/min for all values of E. This
compares well with the 76 Å/min RMS replication error for this data. Surprisingly, the
uniformity of the fitting error indicates that for the purposes of describing data collected
at a single platen temperature with this model, it is not really necessary to know E. The
values of cp (5.8 – 6.1 x 10-9 moles/J, see Fig. 5.14(a)) and a (1.62 – 1.64, see Fig.
5.13(b)) also show very little variation, indicating that one can know these parameters
with some confidence independent of E. As seen in Fig. 5.14(b), the pre-exponential
factor A for the reaction rate k1 shows compensating exponential growth as E increases.
Figure 5.13: (a) Least squares fitting error of the augmented Langmuir-Hinshelwood model to the PE-TEOS data in Fig. 5.8. (b) The temperature model velocity exponent, a
(a) (b)(a) (b)
273
Figure 5.14: (a) The mechanical removal rate coefficient cp and (b) The reaction rate pre-exponential A of the model in this work
Figure 5.15: (a) The temperature increase proportionality constant β and (b) the required reaction temperature rise for the six p × V conditions in the PE-TEOS data
The proportionality factor b (Fig. 5.15(a)) for the temperature rise in Eqn.. (5.11)
decreases with E, indicating that larger values of E correspond to lower required reaction
temperatures. This is seen in Fig. 5.15(b), where the presumed reaction temperature is
plotted as a function of E for all p × V conditions used in the PE-TEOS polishing
(a) (b)(a) (b)
(a) (b)(a) (b)
274
experiments. Fig. 5.15(b) also shows, for comparison, the temperature at which water
would boil. Figure 5.16 compares the model fit with the room temperature (24°C) PE-
TEOS removal rate data at the minimum and maximum values of E considered. It can be
seen that the fit is exceptional over this wide range of E. Figure 5.17(a) shows the model
estimates of the ratio k1/k2 of the chemical rate to the mechanical rate as a function of E
for each p × V condition. Rate ratios are consistently ordered, independent of E, and the
balance of rates ranges from very mechanically limited (k1/k2 » 1, pV2) to slightly
reaction-rate limited (k1/k2 ≈ 0.4 , pV3).
Next, consider the heated and chilled platen PE-TEOS polishing data. In order to
model this data, we use the parameterization A(E), cp(E), a(E), and b(E) found above for
the room temperature data and vary only E and the platen temperature Ta in Eqn.. (5.11).
Since condition pV3 is the most reaction-rate limited (Fig. 5.17(a)), it should provide the
best estimate of E. Based on this E is selected at this condition by minimizing the least
square error between the model and the measured rates at the four platen temperatures.
The model then provides rates at all other values of p × V that serve as an indicator of
predictive capability. Following this procedure, the estimated energy at pV3 was found to
be E = 0.49 ± 0.08 eV (95 percent confidence interval). The resulting rate predictions at
other values of p × V are shown in Fig. 5.18. Except at pV5, where the range of variation
is overestimated, the model provides moderately good extrapolation of the rates observed
on the heated or chilled platen. This agreement can be improved by further optimization
on the entire data set or by separate parameter extraction at each individual temperature.
275
By plotting the modeled removal rate at different platen temperatures against the
measured mean pad temperature, one can extract model predictions of the apparent
activation energy. The result of this is compared with the measured apparent activation
energies in Fig. 5.17(b). It is noted that the apparent activation energies have no
fundamental physical significance – only the real activation energy E has fundamental
physical meaning. The apparent energies come about because the process has a different
balance of mechanical and chemical rates for different combinations of p and V. For k1/k2
» 1, the process is more mechanically limited and consequently has less thermal
sensitivity. For a completely mechanically-limited process, the apparent activation energy
is zero. For a totally reaction limited process the apparent activation energy is E. In the
absence of measurement errors, the apparent energy should lie between zero and E and
should approach E as the process becomes more reaction limited. The ordering of the
apparent energies by k1/k2 in Fig. 5.17(b) is consistent with this picture.
The analysis described above was also applied to the TOX data in Fig. 5.8(a). The
model and measured thermal oxide polish rate data are compared in Fig. 5.19. One can
see that the fit of the model to the room temperature data is accurate and the prediction of
rates at other platen set points, based on an activation energy extracted at the most
thermally limited p × V condition (again pV3), is comparable to or better than the
performance for PE-TEOS. Model parameters are summarized in Table 5.1. The
activation energy for TOX was estimated to be 0.53 ± 0.18 eV (95 percent confidence
interval). Since the confidence intervals for TEOS and TOX overlap, the activation
energies for the two materials are not indistinguishable on the basis of this data.
276
Figure 5.16: Comparison of the fit of the model of Eqns. (5.10) and (5.11) with room temperature PE-TEOS data at the largest and smallest values of E considered
Figure 5.17: (a) Plot of the model estimate of the ratio k1/k2 of the chemical rate to the mechanical rate as a function of E for each p × V condition used in the PE-TEOS data in Fig. 5.8(b). (b) Plot of the measured and calculated apparent activation energies for the PE-TEOS data from Fig. 5.11 as a function of the mean of the ratio k1/k2 at each p × V condition
(a) (b)(a) (b)
277
Figure 5.18: Comparison of the model with PE-TEOS data at different platen temperatures using E from polishing condition pV3 (~31 kW/m2)
Figure 5.19: Comparison of the model in this work (solid symbols) with TOX removal rate data at different platen temperature set points (See Fig. 5.12) using the activation energy at the most thermally limited condition (pV3)
278
Table 5.1: Modeling parameters extracted in the thermal studies from Sandia National Laboratory study. (*) denotes a parameter whose value was assumed rather than extracted. Two sets of parameters are reported for the thermal oxide data from S&H extracted using eight randomly selected points and values extracted using all of the points
5.4.5 Discussion and Conclusions
The Langmuir-Hinshelwood model (Eqn. (5.10)), augmented by the thermal model
(Eqn. (5.11)), provides a simple yet accurate description of both the PE-TEOS and TOX
data reported here. The agreement with data supports our interpretation that these oxide
polishing data span a range of behavior from mechanically-limited polishing to a regime
where thermal effects are significant. One can see that the scatter in the data is actually a
result of competition between the two mechanisms; it is only the use of data visualization
that assumes that the rate depends only on the product p × V that produces the impression
of scatter. The Lim-Ashby plot is more general in that it makes no assumption about the
functional dependence of rate on p and V.
To reinforce this thesis and further test the applicability of the model, the above
analysis was applied to the larger set of thermal oxide polishing data collected by S&H
using a different set of consumables (Stein et al., 2002). The data and fit with the current
Data Set/Figure E (eV) A (moles/m2-sec) cp (moles/J) a b (K/Pa-(m/sec)1-a) RMS Error Å/min (%)TEOS / Fig. 5.8(b) 0.49 2320 5.65E-09 1.63 1.96E-03 103 (9.0 %)TOX / Fig. 5.8(a) 0.53 7970 4.73E-09 1.60 1.76E-03 121 (13 %)TOX [9], 8pt / Fig 5.21 0.53* 153000 5.46E-09 1.71 6.87E-04 52 (3.6 %)TOX [9], 16pt 0.53* 79900 5.31E-09 1.82 1.05E-03 107 (5.8 %)
279
model are shown on a standard Preston plot in Fig. 5.20. In the fitting procedure, half of
the data points were selected at random to use for calibration and half were reserved to
assess the predictive capability of the model. It may also be seen from Fig. 5.20 that the
model agrees well with data at the eight calibration points (RMS error 52 Å/min vs. s =
67 Å/min at the replicated point). Predictions for the eight data points not included in the
calibration fall within the data symbol in seven out of eight cases. The Lim-Ashby plot of
the data is shown in Fig. 5.21. Figure 5.21 clearly has more utility than Fig. 5.20 for
estimating the polish rate at (p,V) combinations not considered in the experiment. Fig.
5.22 shows what the Lim-Ashby plot would have looked like for the experiment had the
polishing behavior been perfectly Prestonian. It can be seen that corresponding contours
are steeper in Fig. 5.22 than in Fig. 5.21. In Fig. 5.23, a map of the ratio of the chemical
rate k1 to the mechanical rate k2 calculated with the model is shown. The map indicates
that the removal process is mechanically limited at conditions on the left side of the map
and that mechanical and chemical rates are nearly balanced on the right side.
While the temperatures implied for the PE-TEOS data by the thermal Eqn.. (5.11) at
E = 0.49 eV may seem high (Fig. 5.15(b)), the temperature rise is consistent with the
magnitude that might be expected of a flash temperature. The form of the temperature
model and magnitudes of the parameters extracted from data are also consistent with a
the more detailed flash heating analysis in Appendix A. It should be noted that
excessively high temperatures would be precluded by temporary, localized vaporization
of the slurry. The observation that the measured pad temperature rise at the trailing edge
is much smaller than the flash temperature is related to the fact that most of the pad
280
surface is not directly heated by friction. The total volume of fluid between the wafer and
pad available to receive the energy also moderates the temperature observed outside of
the wafer: the larger the available volume, the lower the observed pad temperature.
Figure 5.20: Preston plot of TOX polishing data from S&H (open circles and squares). A theoretical fit to the data with the current model is also shown (solid triangles). See also Table 5.1. The fit was performed using a randomly selected subset of the data (circles) – the match with the remaining data (squares) provides a measure of predictive capability
Finally, it was observed that the model presented in this study explains many of the
effects that previous authors have addressed. For example, taken by themselves, data
points at a fixed sliding speed and variable pressure in Fig. 5.8 often extrapolate to a
point on the p × V axis that suggests a nonzero threshold pressure (Fig. 5.24). The current
model suggests that this threshold behavior is not real. Similarly, considering subsets of
data points at constant pressure and variable V, one can find examples of sublinear
281
dependence of rate on V. The present model also provides a unified explanation of this
kind of behavior.
Figure 5.21: Lim-Ashby plot of the thermal oxide polishing data in Fig. 5.20. The grey lines show a triangulation of the individual (p,V) pairs used in the experiment in Fig. 5.20. Contour interval: 500 Å/min
5000 Å/min
4000 Å/min
3000 Å/min
2000 Å/min
1000 Å/min
5000 Å/min
4000 Å/min
3000 Å/min
2000 Å/min
1000 Å/min
282
Figure 5.22: Lim-Ashby wear plot showing how the data from Fig. 5.21 would have looked had the removal rate been perfectly Prestonian (i.e., if all points had been on the regression line with no scatter). The contour lines are linear approximations to hyperbolic arcs of the form p × V = const. The triangles are used for linear interpolation of the measured rates. Contour interval: 500 Å/min
5000 Å/min
4000 Å/min
3000 Å/min
2000 Å/min
1000 Å/min
5000 Å/min
4000 Å/min
3000 Å/min
2000 Å/min
1000 Å/min
283
Figure 5.23: Map of the ratio of chemical rate k1 to mechanical rate k2 derived from the best fit of the Langmuir-Hinshelwood model to the data from Stein and Hetherington (see Figs. 5.20 and 5.21). Material removal is severely mechanically limited in the upper left hand corner of the map. Toward the right side of the map, chemical and mechanical rates are more equally balanced
2510
20
40
80
2510
20
40
80
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Figure 5.24: Apparent pressure threshold behavior at constant V and sublinear velocity behavior at constant p in the PE-TEOS data from Fig. 5.8(b) compared with extrapolations from the current model. The upper model extrapolation is performed at constant pressure (7 PSI) and variable speed. The lower model extrapolation is at constant speed (90 RPM) and variable pressure. The isolated point at p × V~44 kW/m2 (6 PSI, 60 RPM) lies on neither extrapolation because the removal rate depends on p and V individually rather than just on the product p × V. At any fixed p × V, a range of rates is possible
6 PSI60 RPM6 PSI60 RPM
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5.5 Additional Flash Heating Removal Rate Model Applications
In the course of the research done for this chapter, the development and application of
the flash heating removal rate model proved extremely successful in the prediction of
removal rates for ILD CMP results. As a result of these outcomes, the flash heating
model described in Eqns. (5.10) and (5.11) were applied to results from other studies,
specifically those from Chapter 4 and a series of tungsten CMP experiments done at
Sandia National Laboratories. As it will be shown, variations in the consumable sets and
polishing films (i.e., ILD or metal) did not despair the predictive accuracy of the flash
heating removal rate model.
5.5.1 Application of Flash Heating Removal Rate Model on Tungsten CMP
The CMP experiments performed for this study were done at SNL and incorporated
the use of the SpeedFam-IPEC 472 polisher described in Chapter 2.2. Platen temperatures
for this study were controlled using the technique described in Chapter 2.1.9.
The IR camera described in Chapter 2.3.2 was used to record the pad surface
temperature prior to and during polishing. As described in that section, the mean process
temperature of a polish was calculated as the average value of the ten temperature points
shown in Fig. 2.23.
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Wafers used for the CMP experiments were 150-mm diameter silicon wafers with
9000 Å film of blanket tungsten. The polishing time per wafer was 180 sec. On the
primary platen, polishing experiments were run with in-situ conditioning at a conditioner
pressure of 0.5 PSI. Rohm and Haas’s MSW-2000 A and B alumina slurries
(approximately 7 percent solid by weight) were used with a Rohm and Haas IC-1400 K-
grooved polishing pad. The slurry pH was approximately 5 and the slurry flow rate was
255 cc/min for all runs. The following load and rotation rate conditions were used:
• Pad-wafer sliding velocity = 0.5 m/s, Applied wafer pressure = 3 and 7 PSI
• Pad-wafer sliding velocity = 1.00 m/s, Applied wafer pressure = 3 and 6 PSI
• Pad-wafer sliding velocity = 1.51 m/s, Applied wafer pressure = 3, 5 and 7 PSI
All pressure/velocity conditions were run twice in order to assess data repeatability.
All polishing conditions were run at initial platen set point temperatures of approximately
13, 24, 33 and 43°C. Note that the platen set point temperature does not remain constant
during polishing, but provides a desired initial thermal condition for polishing
experiments. Prior to polishing, the pad temperature was monitored until a steady state
temperature was reached for at least 2 minutes. As noted above, the desired platen set
point temperature is not the same as the actual temperature that was recorded using IR
during polishing. The set point temperature creates a general variation in the thermal
environment. Frictional heating induced by polishing causes the local temperature to
exceed the initial set point temperature.
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On the secondary platen, used for buffing, the wafer pressure was 5 PSI and the
carrier and platen rotated at 10 and 100 RPM, respectively. The buffing step was for 30
seconds on a Rohm and Haas Politex pad using a diluted Cabot D7300 fumed silica
slurry (approximately 1 percent by weight). Following each polish, wafers were
mechanically scrubbed using PVA brush rollers in an OnTrak DSS-200 scrubber. Pre-
and post-thickness measurements for the tungsten films were done using a KLA-Tencore
four point probe.
5.5.1.1 Results and Discussion
Similar to the ILD removal rate results obtained from Chapter 5.4, tungsten removal
rate results, shown in Fig. 5.25, also showed deviations from the expected Prestonian
behavior. Using the same physical and theoretical arguments described in Chapter 5.4, it
can be said that the observed non-Prestonian behavior is a result of the competing effects
of the thermo-chemical and mechanical interactions during CMP. A stronger argument
for this hypothesis can be made for tungsten CMP, as well as other metal processes. As
shown in Chapter 5.2, metals such as copper show a more significant dependence on
temperature during CMP because the metal CMP process is predominately driven by the
chemical formation and subsequent removal of an oxidized passivation layer. If the
temperature of the CMP process is increased, the chemical activity at the polishing
interface could impact the formation and removal process favorably (increase removal
rate) or adversely (decrease removal rate).
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Figure 5.25: Tungsten removal rate as a function of p × V and platen temperature set point. Data were not obtained at 25 kW/m2 for platen set points of 13°C and 24°C, as well as 87 kW/m2 for a platen set point of 24°C
The removal rate results shown in Fig. 5.25 show some deviation from what is to be
expected with the rises and falls in process temperature. In general, one would expect that
as the platen temperature increases, the removal rate would increase as well. This was not
the case at several p × V values. One plausible reason for these result variations may be
explained by the fact that these CMP experiments were completed over a six-month time
span. This may suggest that such deviations in the removal rate could be associated to
unnoticeable changes of the tool or consumables. For example, the first set of runs
performed for this study were completed over the summer season, whereas the second set
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of runs were performed over the winter. Based on this, it could have been possible that
the change in ambient temperature could have impacted the slurry or pad performance,
thereby impacting the resulting removal rates.
Using the same analytical principles shown in Chapter 5.2, Arrhenius characterization
of the tungsten process at SNL indicated that the process had an apparent activation
energy of 0.47 ± 0.09 eV. It should be noted that the apparent activation energy is only an
approximation of the true activation energy of the process. When applying the apparent
activation energy of 0.47 eV with the proposed flash heating model described in Chapter
5.4, least square approximations of the data showed that the optimal values for the
applied model were as follows: A = 436.3 moles/m2-sec, cp = 1.52 × 10-8 moles/J, β =
1.40 × 10-3 K/Pa-(m/sec)1-a and a = 0.8.
Using these parameters, the accuracy in predicting tungsten removal rate for all pad
temperatures was approximately 295 Å/min. Figures 5.26 through 5.29 show the relative
accuracy of predicted removal rates with those obtained experimentally. The range in
RMS was from a minimum of 200 Å/min (at Tpad = 13°C) to a maximum of 377 Å/min
(at Tpad = 33°C). The reason for such a large deviation in removal rate predictability (i.e.,
RMS) is directly due to the uncharacteristic removal rate results with temperature over
the six-month span in which experiments were suspended. Regardless of the potential
changes in the experimental conditions during testing, the flash heating model still
outperforms conventional removal rate models with regards to predictive accuracy. When
using Preston’s model, an average RMS value of 460 Å/min was obtained. From a
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modeling perspective, it is clear that the flash heating model provides more accurate
results for tungsten as well as ILD.
Figure 5.26: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 13°C. The RMS between the experimental and theoretical results was approximately 200 Å/min
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Figure 5.27: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 24°C. The RMS between the experimental and theoretical results was approximately 338 Å/min
Figure 5.28: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 33°C. The RMS between the experimental and theoretical results was approximately 377 Å/min
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Figure 5.29: Experimental and theoretical tungsten removal rate as a function of p × V at platen temperature set point of 43°C. The RMS between the experimental and theoretical results was approximately 265 Å/min
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5.5.2 Application of Flash Heating Removal Rate Model on the Freudenberg Pad Study
The CMP experiments performed for this study were done at IPL and incorporated
the use of the scaled polisher described in Chapter 2.1. Platen temperatures for this study
were controlled using the technique described in Chapter 2.1.9.
The IR camera described in Chapter 2.3.2 was used to record the pad surface
temperature prior to and during polishing. As described in that section, the mean process
temperature of a polish was calculated as the average value of the ten temperature points
shown in Fig. 2.23. All other consumable and kinematic polishing conditions have been
described in Chapter 4.3.
Using the underlying principles of the flash heating model presented in Chapter 5.4,
the application of the removal rate and thermal results from these experiments was done
to prove the predictive capability of this model when using an entirely different set of
consumables and experimental conditions. Based on the removal rate results obtained in
Chapter 4.3.2.1, deviations from the expected Prestonian behavior was once again
apparent. This indicated that the apparent, and now predictable, removal rate scatter was
independent of the tool type or consumable sets. As described in Chapter 5.4, one can
again say that the observed non-Prestonian behavior is a result of the competing effects of
the thermo-chemical and mechanical interactions during CMP.
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5.5.2.1 Selection of an Apparent Activation Energy for Modeling
As with prior temperature dependent polishing studies presented in previous sections,
temperature dependent removal rate data enables one to determine an apparent activation
energy, Ea, for the process in question. This parameter can then be used to compare the
thermal sensitivities of removal rate for any process scenario (i.e., different consumables
or polishing films), or it may be applied to the flash heating model shown in Chapter 5.4
as an empirical fitting parameter for removal rate prediction. It was shown in Chapters
5.2 and 5.4 that the apparent activation energy for an ILD process can vary significantly.
Based on the study conducted in Chapter 5.2, an Ea for an ILD process was estimated to
be approximately 0.06 eV. Alternatively, results from Chapter 5.4 showed that the Ea for
an ILD process to be approximately 0.53 eV. This noticeable difference in Ea raises the
question of which is more correct. In theory, the chemical and mechanical processes
involved in ILD polishing should be more or less identical between the two experimental
conditions used. This would mean that the Ea for the overall ILD process should yield
nearly identical results, yet the experimental values obtained in Chapters 5.2 and 5.4 vary
by nearly a factor of nine. The main cause for this is the thermal stability and thermal
range involved during polishing between the two experimental set-ups.
As discussed in Chapter 5.4, the most appropriate selection of an apparent activation
energy for a given experiment would be at the p × V condition which provided the most
chemically limited case based on the flash-heating model presented (i.e., k1 < k2). Under
that scenario, one could determine the apparent activation energy for a process when it
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was the most chemically sensitive. Based on this reasoning, the selection of an apparent
activation energy for the Freudenberg pad study at the most chemically limited cases
proved insufficient.
When calculating the apparent activation energies at most chemically limited
conditions, the Freudenberg pad results generated apparent activation energies which
ranged from 0.053 ± 0.04 eV to 0.182 ± 0.04 eV. Compared to results generated from
Chapter 5.4, these values were significantly lower (this may have been a result of thermal
and kinematic instabilities during testing on the IPL platform). Since these values were
much lower than those previously found (0.53 eV) and since the overall chemical
processes between the film and slurry are considered identical, it could be assumed that
the more appropriate value for Ea would be that which was found on a more stable tool.
Using this reasoning, the Ea applied in the flash heating model for the Freudenberg pad
studies was selected to be 0.53 eV, which was acquired using the SNL set-up.
It should be noted that the actual value of Ea for this model is relative since it is
empirical in nature. In other words, one could also use any alternate value and through
the process of fitting for the other parameters in the model, the parameter values would
compensate for the magnitude of Ea.
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5.5.2.2 Results and Discussion
Using the apparent activation energy of 0.53 eV, the proposed flash heating model
described in Chapter 5.4, yielded optimized parameters for each set of experimental
conditions studied. Table 5.2 shows the approximations of the fitting parameters as a
function of pad type and slurry flow rate. The fitting parameters shown in Table 5.2 were
optimized to provide the lowest RMS error with respect to the experimental data. In
general, there were no noticeable trends with respect to the optimized parameters and pad
groove type, pad thickness or slurry flow rate.
Figures 5.30 through 5.77 show the comparisons in the experimental and theoretical
removal rate results via the traditional Preston plot. In order to quantify the exact
predictive accuracy of the plots shown in Figs. 32 through 77, Table 5.3 was constructed
to show the relative RMS error between the flash heating model and experimental
removal rate results for each polishing condition (pad type and slurry flow rate). In most
cases, the RMS error associated with each data set from the Freudenberg study does not
appear to be as good as those obtained from the results obtained in Chapter 5.4 (average
RMS error = 89 Å/min). This is once again a result of the varying experimental tool set-
ups. The IPL tool set-up is not as stable and consistent as the SNL platform (this is
apparent when one compares the duplication accuracy associated with the removal rate
data shown between the study separate studies). This fact, however, should not be any
indication of model failure.
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Table 5.2: Modeling parameters extracted for the flash heating removal rate model for the results from the Freudenberg pad study
In order to show the effective accuracy of the flash heating model, RMS results from
this model have been compared to the error from other conventional mechanical removal
rate models. Table 5.3 compares the RMS error for the flash heating, Preston, Tseng and
Wang, and Zhang and Busnaina removal rate models. The RMS errors in Table 5.3 are
calculated as an average of each model as they are applied to the experimental data from
all platen set point temperatures. Based on the results shown in Table 5.3, the majority of
Pad Type A (mole / m2-sec) Cp (moles/J) b (K/Pa-(m/sec)1-a) a Ea (eV)
Flat (1.39 mm) 28884 6.91E-09 6.20E-04 1.342 0.53Flat (2.03 mm) 15941 6.66E-09 1.03E-03 1.262 0.53Perf (1.39 mm) 25984 4.63E-09 8.34E-04 1.990 0.53Perf (2.03 mm) 17821 6.34E-09 9.98E-04 0.896 0.53XY (1.39 mm) 38956 7.09E-09 7.73E-04 1.336 0.53XY (2.03 mm) 27195 5.61E-09 6.37E-04 0.906 0.53
Pad Type A (mole / m2-sec) Cp (moles/J) b (K/Pa-(m/sec)1-a) a Ea (eV)
Flat (1.39 mm) 34437 6.71E-09 6.67E-04 1.021 0.53Flat (2.03 mm) 74249 5.55E-09 5.96E-04 1.018 0.53Perf (1.39 mm) 40621 5.16E-09 5.33E-04 1.771 0.53Perf (2.03 mm) 9268 6.50E-09 1.27E-03 0.995 0.53XY (1.39 mm) 54551 7.88E-09 7.85E-04 0.032 0.53XY (2.03 mm) 13288 6.93E-09 9.26E-04 0.803 0.53
Flow Rate = 120 cc/min
Flow Rate = 40 cc/min
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the experimental conditions yield better predictive results when using the flash heating
model.
Table 5.3: RMS errors associated with experimental data and theoretical results obtained from several removal rate models. Errors values represent an average of each model against experimental data for a single polishing condition at all platen set point temperatures
When comparing individual removal rate models with the flash heating model, the
Tseng and Wang removal rate model, which assumes a p5/6 × V1/2 dependence on removal
rate, outperformed the flash heating model in four experimental cases (40 cc/min Flat
2.03-mm, Perforated 1.39-mm, XY 1.39-mm and 120cc/min Perforated 1.39-mm). The
Tseng and Wang model showed the best comparative results among the removal rate
Flash Heating Preston Tseng Wang Zhang BusnainaRMS (Å/min) RMS (Å/min) RMS (Å/min) RMS (Å/min)
Flat (1.39 mm) 173.4 364.8 339.5 452.8Flat (2.03 mm) 252.5 281.8 207.5 293.6Perf (1.39 mm) 215.0 232.8 152.5 244.3Perf (2.03 mm) 138.1 444.9 309.4 228.2XY (1.39 mm) 216.6 204.1 189.3 339.2XY (2.03 mm) 163.0 307.3 193.5 129.2
Flash Heating Preston Tseng Wang Zhang BusnainaRMS (Å/min) RMS (Å/min) RMS (Å/min) RMS (Å/min)
Flat (1.39 mm) 180.9 309.1 293.9 382.0Flat (2.03 mm) 185.3 256.1 273.6 365.1Perf (1.39 mm) 220.9 262.4 162.3 228.5Perf (2.03 mm) 191.0 271.9 315.2 440.9XY (1.39 mm) 252.0 264.1 367.6 485.4XY (2.03 mm) 164.6 174.0 228.8 345.1
Pad Type
Pad Type
Flow Rate = 120 cc/min
Flow Rate = 40 cc/min
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models considered. The Zhang and Busnaina removal rate model as well as the Preston
model outperformed the flash heating model only once. Since the above three models
predict removal rate in a continuous fashion (i.e., they do not allow the possibility for
removal rate scatter), the fact that they occasionally out perform the flash heating model
indicates that the experimental data in those specific cases did not show enough of the
distinct variations of removal rate with temperature and p × V. In other words, the
removal rate data observed from the Freudenberg tests did not show discrete variations
like those seen in Chapter 5.4. It should be noted that this is not to say that these trends
were not present for the Freudenberg tests, but that the trends were not discrete enough.
This lack of distinction in the removal rate results can once again be attributed to the lack
of stability on the IPL tool platform.
When one compares the various models in a general fashion, it can be seen that the
flash heating model has a greater predictive capability than the other mechanically based
removal rate models. For example, if one averages the RMS error for each model and a
single flow rate, regardless of pad type, it may be shown that the RMS error for the flash
heating model is approximately 38 to 57 Å/min better in predictive accuracy. Since the
flash heating model has the capability of predicting removal rate scatter based on
temperature effects during polishing, data which reflects these scattered removal rate
characteristics with temperature distinctly enable the flash heating model to predict the
data in a highly accurate fashion. The fact that the flash heating model has shown
versatility in removal rate prediction with a variety of pad groove types, pad thickness,
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slurry flow rates, film materials, slurry types and polishing tools shows that the flash
heating model has great utility in CMP.
Variations on chemical and mechanical rate constants
On an alternate note, when comparing the ratio of k1/k2 for this study and those
obtained from Chapter 5.4, it is evident that these ratios vary significantly in magnitude.
For example, the range of k1/k2 for the SNL study from Chapter 5.4 was approximately
from 2 to 80, whereas the ratio of k1/k2 for these studies ranged anywhere from 0.4 to
approximately 4. To explain why these ratios are significantly different, one must
consider a few things. First off, the values of k1 and k2 are calculated based on the fitting
parameters found for each set of studies (i.e., A, Ea, Cp, etc.). This alone can affect the
overall magnitude of the ratios. To take another step further, one must consider the
possible physical significance associated with the parameter values. The fact that the ratio
of k1/k2 is much smaller for the Freudenberg study must indicate that the value of ki is
significantly smaller or the value of k2 is greater as compared to those found in Chapter
5.4.
If one considers the argument used for selecting the Ea in this section (i.e., the
chemical processes involved in both studies should be close to identical), then it may be
established that the parameter of ki should not vary dramatically between the two studies.
When comparing mean k1 values, calculations show that both studies have values which
are approximately 10-3 in magnitude. This indicates that the variation in the ratios must
come from possible differences in the k2 parameter.
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The mechanical differences between the study done in Chapter 5.4 and the
Freudenberg study may stem from the pad or the abrasive particles in the slurry. These
two components play a critical role in the mechanics of the CMP process and could have
a bearing on the mechanical contribution to the flash heating model if they are different.
The pads used in both studies varied in grooving as well as material composition.
Although this factor can not be completely characterized due to inadequate knowledge of
the pad composition, it may be considered a player in this issue.
The slurry abrasives, on the other hand, have been characterized and could potentially
explain this k1/k2 phenomenon. The Cabot D7300 fumed silica slurry known to be filtered
prior to use, whereas the Fujimi PL-4217 fumed silica slurry is not. By having a filtered
ILD slurry, the possibility of having large agglomerated particles is far less than that of
an unfiltered slurry. What this may indicate is that an unfiltered slurry may play a greater
mechanical role due to the possible interaction with larger abrasive particles. This could
infact raise the value of k2 for the Fujimi case (i.e., Freudenberg pad study), thereby
leading to a smaller k1/k2 ratio.
Inclusion of COF in flash heating model
The development of the flash heating model described in Chapter 5.4 did not involve
a polishing platform with the capability to acquire COF data. However, the inclusion of a
frictional parameter, if known, within the flash heating model is very possible, although
not critical. Since COF is a parameter that describes the overall normal and shear
mechanical interactions for a specific polishing condition, the possibility to include COF
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into the mechanical portions of the flash heating model is feasible. In doing such, the
mechanical rate constant of the model becomes COFVpCk p ⋅⋅⋅=2 . In addition to this,
the chemical rate constant, k1, may also be changed such that COF is included, however
since the model is used in its compact form, the inclusion of COF is not desired.
Unlike the experiments performed at SNL (Chapter 5.4), polishing experiments
performed for the Freudenberg pad study, on the IPL platform, enabled the acquisition of
real-time COF. This real-time COF could then be included as another input parameter for
model optimization, or be neglected as it has been for the modeling performed in this
chapter. To provide a comparison of modeling results with and without the use of COF
data, Table 5.4 shows a side by side comparison of a select number of experimental
conditions for which COF was included within the flash heating model and not included.
Table 5.4: Flash heating model fitting parameters for select cases of the Freudenberg pad study with the inclusion of COF. This table also includes a side by side comparison of the relative predictive error associated with the model when including and not including COF
Pad Type Flow Rate (cc/min) A (mole / m2-sec) Cp (moles/J) b (K/Pa-(m/sec)1-a) a Ea (eV)Perf (1.39 mm) 40 26263 4.63E-09 7.19E-04 2.101 0.53XY (2.03 mm) 120 13477 6.82E-09 9.31E-04 0.787 0.53
Flash Heating without COF
Flash Heating with COF
Pad Type RMS (Å/min) RMS (Å/min)Perf (1.39 mm) 215.0 260.5XY (2.03 mm) 164.6 165.2
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Table 5.4 presents a new set of fitting parameters that result from the inclusion of
COF in the flash heating model, as well as its effect on removal rate predictability. As
compared to the results shown in Table 5.2 (using no COF), it is obvious that the fitting
parameters do change as a result of COF inclusion. This result is an effect of numerical
compensation during optimization.
Figure 5.30: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min
One apparent issue with using COF as an input parameter in the flash heating model
is the rise in average RMS error associated with removal rate prediction. This is primarily
due to two factors. The first is that an average COF must be considered in order to
establish a single Cp for the model. Since COF varies from run to run, the optimization
for a single Cp value, depends on a singular COF. In this situation, an average COF
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(COFavg) was calculated based on the values achieved from every run and applied to the
overall value of Cp. From this point, k2 can then be calculated using the newly optimized
Cp and the real-time COF values for each run. The slight rise in error stems from the fact
that the ratio of COF to COFavg in the equation for k2, avg
p COFCOFVpCk ⋅⋅⋅=2 , does
not result in unity. The extent of deviation from unity for COF/COFavg varies based on
the stability in COF run to run, and since COF has been shown to change as a result of
changing kinematic conditions, there is little chance that this ratio will ever maintain a
value of one. For this reason, the elimination of COF as input in the flash heating
modeling allows for the elimination of this ratio, thereby resulting in a tighter predictive
fit.
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Figure 5.31: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min
Figure 5.32: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.33: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 40 cc/min
Figure 5.34: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.35: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min
Figure 5.36: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.37: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg flat 1.39-mm pad at a slurry flow rate of 120 cc/min
Figure 5.38: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.39: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min
Figure 5.40: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.41: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 40 cc/min
Figure 5.42: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.43: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min
Figure 5.44: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.45: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg flat 2.03-mm pad at a slurry flow rate of 120 cc/min
Figure 5.46: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.47: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min
Figure 5.48: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.49: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 40 cc/min
Figure 5.50: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min
315
Figure 5.51: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min
Figure 5.52: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.53: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 1.39-mm pad at a slurry flow rate of 120 cc/min
Figure 5.54: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min
317
Figure 5.55: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min
Figure 5.56: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min
318
Figure 5.57: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 40 cc/min
Figure 5.58: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min
319
Figure 5.59: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min
Figure 5.60: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.61: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg perforated 2.03-mm pad at a slurry flow rate of 120 cc/min
Figure 5.62: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min
321
Figure 5.63: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min
Figure 5.64: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.65: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 40 cc/min
Figure 5.66: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.67: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min
Figure 5.68: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.69: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 1.39-mm pad at a slurry flow rate of 120 cc/min
Figure 5.70: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.71: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min
Figure 5.72: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min
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Figure 5.73: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 40 cc/min
Figure 5.74: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 13°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min
327
Figure 5.75: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 24°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min
Figure 5.76: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 33°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min
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Figure 5.77: Experimental and theoretical ILD removal rate as a function of p × V at platen temperature set point of 43°C for the Freudenberg XY 2.03-mm pad at a slurry flow rate of 120 cc/min
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CHAPTER 6 – ENDPOINT DETECTION IN CMP
6.1 Introduction
A brief introduction to EPD was provided in Chapter 1.4.6, in which it was described
that the implementation of a suitable in-line monitoring system during CMP presents
significant advantages for the development and manufacturing environments. As
mentioned earlier, EPD is a technology which enables CMP processes to occur in an
efficient and timely manner. However, the use of EPD for STI CMP processes continues
to pose several problems, mostly due to similarities in the frictional attributes of silicon
oxide and silicon nitride and variations in wafer pattern densities (Brandes, et al., 2003).
Developing a robust approach for EPD in STI CMP applications is critical due to the
potential for reducing the polishing times by reducing the extent of over polishing and
also by reducing the number of wafer reworks. This in turn will result in higher
throughput as well as lower slurry and pad consumption.
In this study we attempt to characterize motor current EPD techniques for STI
patterned wafers by presenting the endpoint and material removal results associated with
four STI structures with varying pattern densities and trench depths. Furthermore, we
attempt to identify the acceptable ranges of STI oxide pattern density variation in which
motor current EPD will suspend polishing within specified process limits. Based on this,
the results will indicate the acceptable regimes of pattern density variation during which
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motor current EPD is successful, and regimes in which pattern density variation
limitations must be set as a result of EPD failure.
6.2 Experimental Approach
This study involved the endpoint characterization of reversed mask processed STI
patterned wafers of four different reticle sets (A through D). Wafers were 150 mm in
diameter. All wafer sets began with 100 Å of a thermally grown pad oxide on a p-type
silicon substrate. This was then followed by a 2500 Å silicon nitride deposition for Sets A
and B, and a 1500 Å silicon nitride deposition for Sets C and D. Sets A and B were then
patterned and etched to obtain a trench depth of 5000 Å. Nominal trench depth for Sets C
and D was 3100 Å. All wafers were then subjected to a sidewall oxide layer growth of
250 Å via dry oxidation. This was followed by plasma-enhanced chemical vapor
deposition of TEOS oxide to achieve trench fill. Structural characteristics of the four sets
are summarized in Table 6.1. Reticles used for these sets provided an adequate range of
oxide density variation (approximately 13.8 to 25.2 %) for a thorough motor current
endpoint investigation. As is evident from Table 6.1, Set D possesses the highest oxide
density variation of all the wafer sets. Based on this it can be said that Set D has the
greatest amount of pattern variation at the die level (i.e., areas with more distinct regions
of high-density structures and low-density open structures), whereas Sets A through C
have less significant changes in the patterned structures on the die level.
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Table 6.1: Oxide and nitride pattern density statistics for the STI patterned wafers used in this study
Sets A through D were planarized using primary and secondary platens of a
Speedfam-IPEC Avanti-472 polisher at SNL (see Chapter 2.2). On the primary platen, to
enhance the signal-to-noise ratio, conditioning was performed ex situ prior to each polish
(4 sweeps at 5 PSI). Cabot’s D7300 fumed silica slurry was used (pH~11) in conjunction
with Rodel’s IC-1400 k-grooved pad. A wafer was set at 7 PSI with a backpressure of 0.2
PSI. Platen and carrier speeds were set at 28 and 32 RPM, respectively. Slurry flow rate
was maintained at 225 cc/min. Polish time (default value of 150 s) was altered in
accordance with the experimental plan. On the secondary platen (intended for buffing),
the wafer pressure was set to 5 PSI with the carrier and platen rotating at 10 and 100
RPM, respectively. The buffing step was 30 s long and involved the use of Fujimi’s
Surfin SSW1 pad and ultra pure water. Following each polish, wafers were mechanically
scrubbed using PVA brush rollers on an OnTrak DSS-200 scrubber. Pre- and post polish
thicknesses of silicon dioxide and silicon nitride films were measured using a KLA-
Tencor UV-1250 ellipsometer.
Oxide (%) Nitride (%) Reticle
Set Density Variation Max Min Mean Density Variation Max Min Mean
Trench
Depth (Å)
TEOS Trench
Fill (Å)
A 13.8 19.4 5.6 11.7 95.8 98.8 3.0 36.2 5000 9000 B 17.4 26.4 9.0 19.0 35.5 53.3 17.8 28.4 5000 9000 C 15.9 30.7 14.8 24.3 59.1 86.1 26.9 41.3 3100 5900 D 25.2 48.4 23.2 37.3 62.2 87.3 25.1 41.4 3100 5900
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The EPD system used in this study has been described in Chapter 2.2.2. Motor
current signals were taken in three modes: platen signal alone (Channel A), platen and
carrier-head signals (Channel A + Channel B), and the ratio of the platen to the carrier-
head signal (Channel A / Channel B). It should be noted that the current signal from the
carrier-head (Channel B) was not considered because previous tests showed unstable and
indistinct signal characteristics during polishing.
6.3 Results and Discussion
The study was performed in three distinct phases. In Phase I, the main objective was
determining the characteristics of endpoint profiling. This was achieved by performing a
complete over polish to determine the general signals obtained for each wafer pattern
under typical polishing conditions. In Phase II, the goal was determining the accuracy of
the timed endpoint by establishing correlations between the approximate times of
polishing and the endpoint signal received from Phase I. Phase III involved endpoint
recipe validation on patterned wafer polishes using endpoint recipes from Phase I and
Phase II.
Phase I involved (a) determining the channel (i.e., Channel A, Channel A + Channel
B or Channel A / Channel B) that provided the most effective signal for EPD, and (b)
establishing the signal scales for the recipes to be viewed during in-line monitoring. To
achieve this, a series of over polish runs was performed to obtain the full signal spectrum
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for Sets A through D. Upon completion of each run, motor current signals such as those
shown in Fig. 6.1 were obtained. As seen in Fig. 6.1, the motor current signal for Set C
generated large changes over the first 100 s of polishing followed by a sharp decline,
indicating a complete over polish (based on post-CMP film thickness measurements).
This same trend was evident for all other wafer sets during the first 100 s. However, in
the range of 60 to 80 s, subtle and characteristic curves were generated based on the
differences in pattern density (note that the scaling provided in Fig. 6.1 does not allow for
clear viewing of the characteristic curves produced for endpoint detection). Analysis of
various signals indicated that only Channel A (the platen motor current) provided the
most distinctive signal change for endpoint detection. The other remaining signals (i.e.,
Channel A + Channel B and Channel A / Channel B) yielded unusable results due to the
lack of distinguishable endpoints.
By analyzing the motor current signals through comparisons with previously
established polish times, initial scaling parameters were established based on correlations
between the two. The purpose of the scaling parameters was to provide an adequate
display of the real-time curves obtained and played no role in the endpoint detection
process.
The objective in Phase II was to determine the endpoint recipe parameters for
effective EPD. To this end, each wafer was polished for a predetermined time and
measured for material removal. Once a wafer was found to be within specified limits for
trench oxide and nitride thickness, the endpoint parameters from that signal were selected
to establish a stopping point for subsequent polishes. These endpoint parameters would
334
later be applied to, and verified for, the signals received from the polish runs in Phases I
and II. Table 6.2 summarizes the timed polish results for Sets A through D. As seen from
the data, all the sets, except Set D, are within specified limits and reach sufficient
planarization in similar times. Based on these results and the repeatability of the motor
current signals, endpoint recipes were formulated to stop at the approximate estimated
times shown in Table 6.2 (with the exception of Set D).
Figure 6.1: Raw platen motor current output (Channel A) for an over polish run from STI patterned wafer Set C
3
3.5
4
4.5
5
5.5
6
0 20 40 60 80 100 120
T ime (seconds)
Raw
Cur
rent
Out
put (
Am
pere
s)
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Although Set D also generated consistent motor current signals, it was apparent that
the wafers required more time for polishing. Following a series of additional polishing
tests, it was estimated that a polish time of 85 s was necessary for satisfactory material
removal. Based on this, attempts at formulating an endpoint recipe for an 85 s polish
proved unsuccessful due to the extreme sensitivity of EPD in the desired time range.
Following several recipe alterations, the most consistent and reliable recipe only achieved
an endpoint of approximately 70 s.
Table 6.2: Trench oxide thickness after timed polishing
Table 6.3 shows the formulated EPD recipes for each wafer set. As seen in Table 6.3,
each wafer set used a specific set of endpoint conditions, each with a generated signal, in
Reticle Set Repetition Time of Run (s) Final Trench Oxide Thickness (Å)
Oxide Spec (Å)
1 5888.38 2 5851.20 A 3
95±1 5745.20
1 6285.98 2 5927.25 B 3
100±2 5958.16
6000
± 2
50
1 3524.62 2 3597.44 C 3
80±1 3560.66
1 3992.11 2 4036.86 D 3
65±10 3953.32
3500
± 2
50
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order to suspend polishing. As polishing occurs, a signal is generated and analyzed by the
Luxtron tool using a viewing window. Each viewing window was specified with a
window width (scaled to polishing time) and window half-height (scaled to a percentage
of the total signal amplitude). Note that each window begins with its left edge centered on
the point at which the signal intersects any boundary on the previous window (Fig. 6.2
shows the window features described above). By using a set of window dimensions, the
tool was then able to analyze each on-going polishing signal in a series of finite periods.
Table 6.3: Window parameters for EPD of STI patterned wafer Sets A through D
In order to analyze the signal within each viewing window, a signal type that was
most sensitive to the acquired signal was selected. As seen in Table 6.3, the
“Interference” and “Falling Slope” signal types were used. By definition, an
“Interference” signal detects oscillations within each window and a “Falling Slope”
signal detects a signal that is dropping in magnitude within each window. Beyond this,
one also had to specify the point at which a signal should be stopped. To achieve this for
Reticle Set Signal Type Stopping
Point InitiationWindows
TerminationWindows
Window Width
Window Half-
Height A Interference End of Oscillation N/A 6 5 s 5.0% B Falling Slope End of Slope 3 4 6 s 3.1% C Falling Slope End of Slope 3 5 6 s 5.0% D Interference End of Oscillation N/A 5 6 s 5.0%
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the “Interference” signal type, one could specify the end of an oscillation, period, a
specific number of peaks or valleys within an oscillation or a specific number of peaks
and valleys combined. For a “Falling Slope” signal type, one could specify the detection
of an onset of a falling slope at the beginning or the end of a signal. In this study, it was
determined that “End” stopping conditions were most effective for the signals obtained.
Figures 6.3 and 6.4 show examples of signal termination for “Interference” and “Falling
Slope” signal types, respectively. Finally, in order to ensure consistency and reliability
for a recipe during an on-going signal, a number of initiation and termination windows
had to be established. Initiation and termination windows describe the number of
windows required to achieve the signal type and stopping conditions for each recipe,
prior to the termination of a polish (it should be noted that no initiation windows are
required when detecting oscillations, whereas initiation and termination windows are
required when detecting a falling slope).
Figure 6.2: Endpoint detection viewing window with specified dimensions
Signal position at start of window
Window Width (time)
Half-Height (Amplitude)
Signal position at start of window
Window Width (time)
Half-Height (Amplitude)
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Figure 6.3: Typical conditions for endpoint detection using an “Interference” signal type and End of oscillation stopping point
Figure 6.4: Typical conditions for endpoint detection using a “Falling Slope” signal type and End of slope stopping point
Figures 6.5 and 6.6 show examples of reprocessed signals for each wafer set in this
study. The x-axis and y-axis in Figs. 6.5 and 6.6 represent polish time (in minutes) and
motor current signal amplitude from the platen, respectively. It should be noted that the
Optima 9300 system automatically stopped each signal at the desired polishing time with
a reproducibility of within 5 s.
Polishing Time (s)
Sign
al A
mpl
itude
Polishing Time (s)
Sign
al A
mpl
itude
Polishing Time (s)
Sign
al A
mpl
itude
Polishing Time (s)
Sign
al A
mpl
itude
339
The third and final phase of this study was an evaluation of the formulated motor
current EPD recipes developed in Phase II. In brief, the EPD system was used to
terminate the polishing process and the resulting wafers were measured for accuracy and
repeatability. Table 6.4 summarizes the polishing results obtained using the endpoint
recipes described in Table 6.3 (note that the number of repetitions exceeded the number
shown in Table 6.4). It should be noted that all polishes resulted in within-wafer non
uniformity values of less than 7 percent.
Figure 6.5: Motor current signal for polished wafer from Set A with an applied endpoint recipe (left). Motor current signal for polished wafer from Set B with an applied endpoint recipe (right)
Time (s) Time (s)
Sign
al A
mpl
itude
(mA
)
Sign
al A
mpl
itude
(mA
)
Time (s) Time (s)
Sign
al A
mpl
itude
(mA
)
Sign
al A
mpl
itude
(mA
)
340
Figure 6.6: Motor current signal for polished wafer from Set C with an applied endpoint recipe (left). Motor current signal for polished wafer from Set D with an applied endpoint recipe (right)
As shown in Table 6.4, EPD recipes for Sets A through C allowed polishing to occur
until an adequate stopping point was detected. Ellipsometric measurements indicated that
resulting trench oxide removal rates were within specified value ranges and allowed for
little or no nitride removal.
In spite of the successful and repeatable results for Sets A through C, the results for
Set D indicated unsuccessful EPD. Trench oxide removal data showed that the endpoint
limit for these wafers was prematurely triggered by the Optima 9300. Despite further
polishing attempts using altered recipe parameters, the motor current signal towards the
Time (s) Time (s)
Sign
al A
mpl
itude
(mA
)
Sign
al A
mpl
itude
(mA
)
Time (s) Time (s)
Sign
al A
mpl
itude
(mA
)
Sign
al A
mpl
itude
(mA
)
341
later stages of the polish appeared too sensitive for detection. For example, an increase in
the number of termination windows (i.e., an analysis window defined by a time width and
signal amplitude height selected to identify the desired signal behavior for endpoint
detection) from 5 to 6 would frequently allow polishing to continue beyond previously
estimated termination times.
Table 6.4: Motor current endpoint results for STI patterned wafer Sets A through D
To lend a possible explanation of endpoint failure for Set D, a comparison between
Sets C and D can be drawn based on their structural similarities and the endpoint success
of Set C. As seen from Table 6.1, Sets C and D showed no significant variation in nitride
Reticle Set Repetition Polish Time
(s)
Final Nitride
Thickness (Å)
Final Trench Oxide
Thickness (Å)
Oxide
Spec (Å)
1 90 1788.74 5857.89
2 96 1969.22 6116.38 A
3 113 1783.02 5751.31
1 103 2017.05 6240.69
2 115 1879.99 5964.09 B
3 108 1879.92 6001.94
6000
± 2
50
1 87 1055.14 3545.55
2 84 973.99 3641.28 C
3 89 933.55 3494.39
1 77 1192.6 3981.19
2 77 1076.38 3970.73 D
3 80 1020.61 3844.20
3500
± 2
50
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density, but showed considerable differences in oxide density. Figures 6.7 and 6.8 are
original density distribution histograms for Sets C and D, respectively. The effective
pattern density maps in the aforementioned figures were produced using an elliptical
weighting function with a planarization length of 3.5 mm and a similar methodology to
that used by Lee et al., (Lee et al., 2000). Note that Set C (Fig. 6.7) has an oxide density
variation that ranges between 14.8 and 30.7 percent, whereas Set D (Fig. 6.8) has an
oxide density range between 23.2 and 48.4 percent. This signifies a sharp contrast in the
consistency of die-level oxide density. Due to the larger oxide density variation of Set D,
the die has more distinct regions of high-density structures (i.e., SRAM cells) and low-
density, open structures. In comparison, the oxide density variation for Set C presents a
more consistent, or flowing, density structure. Based on the contrasting density structures
of Set D, it is possible for the faster polished, low-density regions to trigger the endpoint
prior to adequate polishing of the high-density regions.
One possible solution for endpoint correction would be a dual stage process. This
would involve allowing the existing recipe for Set D to stop the polish prematurely at
around 70 s as an initial polishing stage, and then program the monitoring tool to allow
for a secondary timed polish stage of 15 s.
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Figure 6.7: Pattern density distribution for STI patterned wafer Set C
Figure 6.8: Pattern density distribution for STI patterned wafer Set D
Dis
trib
utio
n Fu
nctio
n
Density
Dis
trib
utio
n Fu
nctio
nD
istr
ibut
ion
Func
tion
Density
Density
Dis
trib
utio
n Fu
nctio
n
Density
Dis
trib
utio
n Fu
nctio
n
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6.4 Concluding Remarks
Patterned wafer sets ranging from 13.8 to 25.2 percent in oxide density variation were
analyzed using the Luxtron Optima 9300 in-line monitoring tool. By analyzing distinct
motor current signals generated during polishing, endpoint parameters were established
and verified for each of the various patterned wafer sets. Based on the results, successful
endpoints were detected for wafers with oxide density variations ranging from 13.8 to
17.4 percent (i.e., wafer sets A through C). Wafer set D, which had the highest mean
oxide density (25.2 percent) proved inaccurate for EPD. It has been postulated that this
failure was caused by false signals generated by variations in polishing rates resulting
from discrete dissimilarities in oxide density regions on the die-level. Although one could
remedy premature EPD by introducing a secondary timed polishing stage, it would be
better to obtain a single recipe for polishing completion.
From the results presented in this study, one could hypothesize that there is an upper
limit of oxide density variation (between 15.9 and 25.2 percent) that a STI wafer can
have before motor current endpoint failure occurs. Establishing this density limit could
lead to more stringent limits on STI pattern designs, but allow for more reliable EPD
systems.
The success of endpoint detection for Sets A through C presents several
considerations with regards to CMP consumables minimization and overall cost of
ownership. For a typical STI CMP process, in the absence of in-line endpoint monitoring
system, several CMP steps must be completed for a satisfactory outcome. In high-volume
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manufacturing, planarity is usually achieved through an initial polish, followed by film
thickness metrology and, if needed, a ‘rework’ polishing step to remove any residual
material. Rework times and conditions, in general, vary depending on the remaining
material thickness following the initial polish. Reworks, which may need to be performed
on roughly 10 percent of all wafers in production, typically range from 15 seconds to 1
minute. This translates into longer processing times and additional consumables usage.
Although rework polishes are not commonly mentioned in industry, most IC fabrication
facilities implement them to meet module line-yield goals.
With the utilization of an EPD system, the number of reworks could be reduced thus
resulting in lower slurry, pad and conditioner usage. Based on the typical polish
conditions for the wafer sets used in this study, successful EPD was seen to reduce polish
times by an average of 13 seconds per wafer. Considering a typical slurry flow rate of
225 cc/min, it is estimated that slurry usage could be reduced by roughly 15 percent per
polish (along with a comparable reduction in pad usage). Moreover, a robust EPD
technique in high-volume manufacturing can potentially reduce reworks by a factor of
two (i.e., from 10 to 5 percent). Using a simple cost-of-ownership model (Olsen, 2002),
the potential slurry and pad savings (minus initial capital investment for the EPD
systems) associated with an STI module is estimated to be roughly $200,000 per year
(200-mm wafer factory operating at 5000 wafer starts per week).
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CHAPTER 7 – CONCLUSIONS AND FUTURE WORK
The various studies conducted during the coarse of this work ranged in a variety of
subjects associated with CMP. Topics included the impact of applied wafer pressure
effects during CMP, the impacts of pad type, tool kinematics and pad temperature during
CMP, the role of temperature in CMP and EPD applications for an effective CMP
process. The outcomes related to each of these subject matters ranged anywhere from
possible design considerations for improved consumables to direct conclusions regarding
the chemical and mechanical processes involved within each study.
Considering the range and diversity of the separate works done for this dissertation,
the primary conclusions regarding each study have been divided per subject matter.
• Impact of Wafer Geometry and Thermal History on Pressure and von Mises
Stress Non-Uniformity During CMP
Results demonstrate that variations in wafer geometry, as measured by the
overall shape (i.e., extent and direction of bow), nominal diameter and thermal
treatment of the wafers, can significantly affect the extent of pressure experienced
by the wafer during CMP. Based on the variation of pressure incurred by the
wafer from the center to the edge of the wafer, it may be shown that removal rate
can vary significantly across the wafer surface depending on the extent and
direction of wafer bow, the wafer-ring gap size and the thermal history of the
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wafer (i.e., it was shown that the removal rate along the edge of a wafer can range
from 400 to 800 Å/min for a concave, thermally untreated wafer having a wafer-
ring gap size of 1.0 mm).
Results also demonstrated that variations in wafer geometry can significantly
affect the extent of WIWNU for ILD CMP. In addition, these results draw
attention to the importance of adopting tighter manufacturing control limits in
order to minimize WIWNU issues during CMP.
• Estimating the Effective Pressure on Patterned Wafers during STI CMP
This study presented a first generation method for approximating the effective
pressure experienced by STI patterned wafers during CMP. A root finding
technique enabled the calculation of the effective (or envelop) pressure for a
variety of pattern density wafers using removal rate data acquired from the
polishing tests. Results showed that regardless of applied wafer pressure, the ratio
of the derived effective pressure to applied wafer pressure was relatively
consistent. The stability of these ratios indicated that in cases of a five-fold (i.e.,
from 10 percent to 50 percent) or nine-fold increase in pattern density (i.e., from
10 percent to 90 percent), the effective pressure experienced during polishing was
not impacted by the pattern density in a proportionate manner. These findings are
believed to have significant implications in all CMP processes where shear force
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needs to be controlled or minimized (i.e., for copper or low-k applications) for a
wide range of pattern densities.
• Impact of Tool Kinematics, Pad Geometry and Temperature on the Removal Rate
and Process Tribology During ILD CMP
The Freudenberg pad study was developed to provide a complete
characterization of ILD CMP with respect to changes in pad grooving (i.e., flat,
perforated and XY), pad thickness, platen set point temperature, slurry flow rate
and kinematic process conditions.
Material removal rate results showed that despite the pad groove type or pad
thickness, removal rates appeared linearly dependent with each set of sliding
velocities used during testing. Removal rate results also showed that slurry flow
rate did not appear to have a significant impact on material removal for all pad
types. This fact was also confirmed via regression analysis of the data acquired in
the study. Moreover, results from this analysis showed that p × V had the greatest
impact on removal rate followed by pad groove type.
When focusing on pad temperature rises as a function of various kinematic
conditions and slurry flow rates appeared to have no significant impact on pad
heating. The XY-groove pad showed the lowest rise in pad temperature as
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compared to the flat and perforated pads. This is believed to be a result of the
pads ability to cool the pad-wafer interface via enhanced slurry transport.
Finally, all polishing conditions showed that regardless of pad groove type,
pad thickness, pad temperature or slurry flow rate, all of the tribological
mechanisms occurred within the boundary lubrication regime.
• Arrhenius Characterization of ILD and Copper CMP Processes
By modifying the generalized Preston’s equation to employ an Arrhenius
argument, this study introduced a new parameter described as the combined
activation energy. Based on this new parameter, the impacts of pad temperature
on the chemical and mechanical facets of CMP were capable of being quantified
into a single defined value, which showed the differences between various
dependencies arising from the use of different of consumable sets. For ILD
polishing, results indicated a combined activation energy of 0.06 eV for the
process. Copper polishing resulted in a combined activation energy of 0.52 eV,
which indicates a more thermally dependent process. These results indicated that
information regarding the relative magnitude of the thermally dependent and
thermally independent aspects of the ILD and copper CMP processes (as triggered
by controlled thermal changes in the system) can be critical in designing novel
pads and slurries with controlled chemical and mechanical attributes.
350
• Effect of Process Temperature on Coefficient of Friction during CMP
Based on a series of controlled temperature polishes, COF results indicate that
a rise in polishing temperature creates a rise in shear force for both ILD and
copper CMP. DMA results yielded supporting evidence towards this observation.
It was also shown that the rise in COF with pad temperature could partially be
explained through a proportionality relationship of shear force and tan δ.
• Revisiting the Removal Rate Model for Oxide CMP
This study sought to explain removal rate trends and scatter in thermal silicon
dioxide and PE-TEOS CMP results using an augmented version of the Langmuir-
Hinshelwood mechanism for ILD polishing. The proposed model combined the
chemical and mechanical facets of ILD CMP and hypothesized that the chemical
reaction temperature is determined by transient flash heating. When using the
newly developed model with experimental results, the agreement between the
model and data suggests that the main source of apparent scatter in removal rate
data plotted as rate vs. p × V, is competition between mechanical and thermo-
351
chemical mechanisms. Based on this, a method of plotting and visualizing
removal rate data was introduced.
• Additional Flash Heating Applications
This study adopted the previously described flash heating removal rate model,
and sought to apply it to experimental data taken from both tungsten and ILD
films. Results showed that the flash heating model could once again discriminate
scattered data based on changes in the process temperature. Removal rate and
thermal instabilities that resulted from errors associated with tool stability and
temperature control techniques created several sources for poor model prediction,.
However, when considered alternate removal rate models, the flash heating model
outperformed the predictive capability of the rest a majority of the experimental
cases.
• Endpoint Detection in CMP
This study investigates the feasibility and environmental implications of
motor current endpoint detection for STI CMP processes. Results indicated that
repeatable motor current endpoint detection can be achieved for STI wafers with
352
oxide pattern density variations of up to 17.4 percent. Furthermore, results show
that a dependence exists between the STI oxide pattern density variation and
motor current endpoint success during polishing. Due to the outcomes of this
study, a suitable motor current EPD system could yield successful termination
points for STI polishing, as well as reduce the need for polishing reworks. It was
estimated that the use of a successful EPD system could reduce slurry usage by as
much as 15 percent per polish and allow savings of roughly $200,000 per year in
slurry and pad consumables for a typical IC manufacturing facility.
7.1 Future Works
Considering the variety of work conducted for this dissertation, several future studies
could be proposed for consideration. Chief consideration should be given to the
continuation of the thermal work described in Chapter 5. Further studies should be
conducted on stable industrial tools to observe the thermal sensitivity of various polishing
scenarios (i.e., films, pads, slurries, kinematic conditions, etc.). Two potential focuses
include thermal studies with respect to copper and tungsten films.
Coupled with these studies is the further application of the flash heating removal rate
model proposed in Chapter 5. Providing ample proof of this model with a range of
various metal and dielectric films could provide greater insight towards the actual process
mechanisms during CMP. In addition to this, further verification of the flash heating
353
model could provide greater predictive capabilities in a research or industrial setting that
could eventually lead to more efficient processes.
Future work should also be focused on the contribution of conditioning of existing
processes. Specific aspects of this could include the coupled effects of diamond
conditioning and pad temperature on pad wear and polishing performance, as well as the
effects of alternate pad conditioning techniques on polishing performance.
354
APPENDIX A – ADDITIONAL PROOFS FOR FLASH HEATING REMOVAL RATE MODEL
A.1 Modeling Proof (Courtesy of Len Borucki)
For the following proof, one must assume that heating is mechanical in origin and
estimate the flash temperature T averaged over the wafer surface. At a fixed point on the
wafer, the largest temperature excursions occur during encounters with slurry particle-
laden pad asperities. If temperature continuity applies during these encounters, then the
temperature rise of the wafer above its body temperature will depend on the previous
contact and heating history of the asperity. It will also be assumed, for simplicity, that
fresh slurry in the bow wave cools asperities sufficiently on each pad rotation that only
the current interaction with the wafer need be considered. If an asperity at radius R from
the pad center has entered the wafer at polar angle -ψ0(R) and is currently at (R,ψ) under
the wafer (Fig. 1.19), then the contact time τ at this point is
pR Ω+= /)(),( 0ψψψτ , (A.1)
where Ωp is the pad rotation rate. After contact for time τ at mean real contact pressure
pa and constant frictional power density µkpaV, the asperity tip temperature rise θ(τ) is
then (Cowen et al., 1992),
2/1)( ττθ C= , (A.2)
where,
355
p
akp
CVp
Cπκρ
µγ2= . (A.3)
In Eqn. (A.3), κ, ρ, and Cp are the thermal properties of the pad, µk is the kinetic COF
and γp is the fraction of the total frictional power density that is conducted into the pad
rather than to the slurry or wafer. From Eqn. (A.1 – A.3), the desired mean temperature
rise of asperity tips in contact with the wafer is
∫∫ ∫ ∫∫ ∫+
− −
+
− −
+Ω
=== dRdRr
CdRRdCr
dAr
ww
ww
ww
ww
rc
rcpw
rc
rcww
ψψψπ
ψτπ
τθπ
θψ
ψ
ψ
ψ
0
0
0
0
2/102/12
2/122 )(1)(1
= ∫
+
−
ww
ww
rc
rcw
w dRRr
cV
C 2/302
2/1
2/1 )2(32
ψπ
, (A.4)
where one has to use the fact that pwcV Ω= when the pad and wafer co-rotate (Patrick et
al., 1991). The expression in square brackets in Eqn. (A.4) depends only on the wafer
radius and center location. Calling this quantity ),( ww crζ , one then has the absolute mean
temperature T as
2/1−+=+= CVTTT bb ζθ
pVV
ppC
T ap
p
kb 2/1
)]/([2 γπκρ
ζµ+= , (A.5)
where Tb is the mean body temperature. Because of the factor V-1/2 in Eqn. (A.5), the
mean flash temperature appears to vary like pV1/2. However, the factors pa/p and pγ in
square brackets also may depend on V. For example, pa/p would decrease with increasing
V if positive fluid pressures were to develop under the wafer and the velocity were to
increase enough to initiate a transition from boundary lubrication to hydroplaning. While
356
possible on a flat pad, the experiments here were performed on concentrically grooved
pads that prevent significant fluid pressure development over the range of sliding speeds
used. Thus, we take pa/p to be constant.
Now consider pγ . Heat partitioning was evaluated using a 3D finite element model for
lubricated contact between a pad asperity tip and a smooth SiO2-coated silicon wafer in
relative motion. Because of our Lagrangian approach, one may consider the asperity to be
fixed and the wafer to be a slider with velocity V. The wafer at the leading edge of the
contact is held at a fixed temperature to simulate the arrival of as-yet unheated wafer
material. Heat from friction that is conducted into the wafer is advected toward the
trailing edge with velocity V. Heated slurry is also advected with a velocity that varies
linearly between zero and V in the shear layer, in which the power density µkpaV is
assumed to be evenly dissipated. The lubricating slurry was assumed to be a uniform
nanofilm with thickness on the order of the mean slurry particle size ( approximately 10
to 125 nm). Several film thicknesses were examined because the actual nano-film
thickness is unknown. Under these conditions, the 3D heat equation was integrated until
heat fluxes reached steady state (approximately 0.5 ms), after which the partition factors
were evaluated. The thermal conductivities used were 156 W/m-K for silicon (298 K),
1.4 W/m-K for SiO2, 5.98x10-2 W/m-K for slurry (treated as water) and 0.22 W/m-K for
the polyurethane pad.
For simplicity, the contacting face of the pad asperity was taken to be a square instead
circular. Contact area sizes and real contact pressures were estimated using pad physical
data and Greenwood and Williamson theory. First, it should be noted that pad surface
357
height probability density functions (PDFs) often have an exponential tail (Fig. A.1)
(Borucki et al., 2004). Therefore it is assumed that the summit height PDF to have the
form )/exp()( λφ zBz −= for z > z0. If d is the equilibrium contact height of the wafer at
applied nominal pressure p, then it follows from Greenwood and Williamson theory that
p and d are related by
2/12/5*2/12/32/1
*
/)()()(34
ssds
s dEdzzdzEp κφληπφκ
η∫
∞=−= , (A.6)
if d > z0. In Eq. (A.6), )1/( 2* ν−= EE is the effective pad modulus, ηs is the summit
density and κs the mean summit curvature. At height d, an asperity of undeformed height
z>d has contact area sa dzr κππ /)(2 −= from Hertzian theory. The expected contact area
is then
sd a ddzzr κφπλφπ /)()( 22 =∫∞
. (A.7)
We pick our contact area square side length s to correspond to the mean contact area,
sds κφπλ /)(22 = . (A.8)
Combining Eqns. (A.6) and (A.8), φ(d) may be eliminated to obtain the more useful
formula
2/12/1
2/1
*2 −= s
sEps κ
ληπ . (A.9)
Similarly, the mean real contact pressure corresponding to the mean contact area is
4/32/14/14/5
2/1*
34
ss
a
pE
pp κ
ηλπ
= . (A.10)
358
Formulas (A.9) and (A.10) express s and pa/p in terms of the known nominal pressure
p and the physical parameters E*, λ, ηs and κs. Here, p = 7 PSI is used and corresponds to
one of the experimental loads in this study, E=285 MPa, ν=0.5, λ=2.0 µm (Fig. A.1), and
ηs =2.0x108 /m2 (Elmufdi et al., 2004; Shan et al., 2000). The mean asperity tip curvature
κs depends on pad conditioning. If one takes κs to be a variable in Eqns. (A.9 and A.10)
and considers values from κs =2.0x104/m to 5.0x105/m, then one can find that that s
varies from 2.37 µm to 1.06 µm and pa/p from 89.4 to 1000 (Shan et al., 2000).
Based on the finite element results, we find that as V increases, the wafer side of the
lubrication layer becomes cooler due to heat advection, a larger fraction of the total heat
flows toward the wafer, and pγ therefore drops. Figure A.2(a) plots pγ as a function of V
for several contact sizes and lubrication layer thicknesses. Since pγ was only weakly
influenced by the lubricating film thickness, we report results mainly at 50 nm. In Fig.
A.2(a), pγ is seen to be sensitive to V and to approximately follow a power
law, epp V/1γγ = , where 1
pγ and e both depend on s. A power law fit is accurate except
when s and V are both small. From Fig. A.2(a) we have 431 1014.91032.2 −− −= xsxpγ and
08.1/48.1 se = , where s is in microns. Based on this, one can take
aape
apsp VppV
ppV
pp −+ == )/(/]/[ 1
2/1
1
2/1 γγγ
, (A.11)
where a=1/2+e and write Eqn. (A.5) as
ab pVTT −+= 1β , (A.12)
where
359
p
apk
Cpp
πκργζµ
β/2 1
= . (A.13)
Equation (A.12), with the body temperature approximated by the ambient
temperature, is the compact thermal model in this paper. Note that the experimental
exponents a in Table 5.1 are consistent with the calculated values of e in Fig.A.2(b).
Figure A.1: Polishing pad scanning profilometry data showing evidence of an exponential right hand tail (Borucki et al., 2004)
360
Figure A.2: (a) Pad heat partition factors as a function of sliding velocity and asperity contact dimension. (b) Pad heat partition factor proportionality constant and velocity exponent
(a) (b)(a) (b)
361
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